Paper Citation Record · LEDGER

Koszul Graded M\"obius Algebras and Strongly Chordal Graphs

As of 19 August 2026, this Paper Citation Record lists 47 of 47 outbound references and 0 inbound Pith citation observations for arXiv:2412.18499.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2412.18499 v1

Coverage vector

measured 47 of 47 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-11T04:58:50.325604Z

measured 47 of 47 standing notices

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Source: scholarly_work_events, retraction_status_cache, observed 2026-08-19T06:32:44.657259+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

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measured 0 of 1 external citation measurements

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Source: cited_works

Reference resolution

47 of 47 outbound references displayed

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verified fuzzy40
unresolved7
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External citation measurements

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Outbound references

Observation 3f67ea3d-0a01-4248-afe7-6b5e8df5bc3a · outbound

This paper cites The closure of a linear space in a product of lines.

Koszul Graded M\"obius Algebras and Strongly Chordal Graphs The closure of a linear space in a product of lines

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T04:58:50.847901Z

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Observation 45224184-ce75-4c17-aa65-39a6b82901b7 · outbound

This paper cites Singular Hodge theory for combinatorial geometries.

Koszul Graded M\"obius Algebras and Strongly Chordal Graphs Singular Hodge theory for combinatorial geometries

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-11T04:58:50.156764Z

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Unavailable: canonical work link unavailable.

Observation 10b6e4b0-4b88-4d66-8caf-8491a546f95b · outbound

This paper cites Matherne, Nicholas Proudf oot, and Botong W ang.

Koszul Graded M\"obius Algebras and Strongly Chordal Graphs Matherne, Nicholas Proudf oot, and Botong W ang

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T04:58:50.837600Z

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Observation 02becc1f-8e33-4c36-97bf-19b909db6ab3 · outbound

This paper cites The homology and shellability of matro ids and geometric lattices.

Koszul Graded M\"obius Algebras and Strongly Chordal Graphs The homology and shellability of matro ids and geometric lattices

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T04:58:50.826999Z

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Observation c6b8fabe-1e2e-48af-9377-027da046d9ad · outbound

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Koszul Graded M\"obius Algebras and Strongly Chordal Graphs Unresolved cited work

Reference 5

Resolution: unresolved; raw_fallback, observed 2026-08-11T04:58:50.816445Z

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Observation d1f0a054-8b14-4bb0-adaf-872e4705892d · outbound

This paper cites The pinched Veronese is Koszul.

Koszul Graded M\"obius Algebras and Strongly Chordal Graphs The pinched Veronese is Koszul

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T04:58:50.805757Z

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Observation a64f65f2-d8dd-4777-a8dc-c2edc7f27dca · outbound

This paper cites Koszul property of proje ctions of the Veronese cubic surface.

Koszul Graded M\"obius Algebras and Strongly Chordal Graphs Koszul property of proje ctions of the Veronese cubic surface

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T04:58:50.794415Z

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Observation 8cf76101-f1b9-4179-a3e8-914c7aeed7ea · outbound

This paper cites K oszul algebras and regularity.

Koszul Graded M\"obius Algebras and Strongly Chordal Graphs K oszul algebras and regularity

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T04:58:50.782752Z

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Observation ecd68811-b255-42c9-82b7-50ffd4677f28 · outbound

This paper cites How is a c hordal graph like a supersolvable binary matroid? Discrete Math.

Koszul Graded M\"obius Algebras and Strongly Chordal Graphs How is a c hordal graph like a supersolvable binary matroid? Discrete Math

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T04:58:50.771700Z

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Observation 37b97cac-f342-472a-9f35-fee82749de5c · outbound

This paper cites Koszul algebras and their syzygies.

Koszul Graded M\"obius Algebras and Strongly Chordal Graphs Koszul algebras and their syzygies

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T04:58:50.760475Z

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Observation 383b8ab5-d9d9-4144-b9ed-3e251a20465e · outbound

This paper cites Supersolvability of built lattices and K oszulness of generalized Chow rings, 2023.

Koszul Graded M\"obius Algebras and Strongly Chordal Graphs Supersolvability of built lattices and K oszulness of generalized Chow rings, 2023

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T04:58:50.749670Z

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Observation 4dade612-894b-413a-9b5d-f2c459882e11 · outbound

This paper cites Gr ¨ obner ﬂags and Gorenstein algebras.

Koszul Graded M\"obius Algebras and Strongly Chordal Graphs Gr ¨ obner ﬂags and Gorenstein algebras

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T04:58:50.738965Z

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Observation d4f4bf40-0d05-4b7e-8fd2-b4415d9f1526 · outbound

This paper cites Homotopy invariants for M 0,n via Koszul duality.

Koszul Graded M\"obius Algebras and Strongly Chordal Graphs Homotopy invariants for M 0,n via Koszul duality

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T04:58:50.728491Z

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Observation 12c14a95-647f-4e32-a1e2-2ab25e930e75 · outbound

This paper cites Line-closed matroids, quadratic algebr as, and formal arrangements.

Koszul Graded M\"obius Algebras and Strongly Chordal Graphs Line-closed matroids, quadratic algebr as, and formal arrangements

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T04:58:50.718133Z

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No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation a06a2a5a-499b-4229-8c93-b68bb571734a · outbound

This paper cites Characterizations of strongly chordal graphs.

Koszul Graded M\"obius Algebras and Strongly Chordal Graphs Characterizations of strongly chordal graphs

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T04:58:50.707405Z

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Observation 3870a7d5-b707-4783-89ac-c0a213fbb202 · outbound

This paper cites Matherne, Matthew Stevens, and L orenzo Vecchi.

Koszul Graded M\"obius Algebras and Strongly Chordal Graphs Matherne, Matthew Stevens, and L orenzo Vecchi

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T04:58:50.697015Z

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No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 95635836-087a-4b51-aad9-d0118e028d75 · outbound

This paper cites Koszul algebras.

Koszul Graded M\"obius Algebras and Strongly Chordal Graphs Koszul algebras

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T04:58:50.686706Z

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No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation b441fef5-0604-4f22-be1f-efd92b15a3c9 · outbound

This paper cites Chow rings of toric varieties deﬁned by atomic lattices.

Koszul Graded M\"obius Algebras and Strongly Chordal Graphs Chow rings of toric varieties deﬁned by atomic lattices

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T04:58:50.676282Z

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No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 41956e32-969b-4b68-8b59-1b950d69867a · outbound

This paper cites On the M¨ obius algebra of a partially ord ered set.

Koszul Graded M\"obius Algebras and Strongly Chordal Graphs On the M¨ obius algebra of a partially ord ered set

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T04:58:50.666682Z

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Observation 35194a96-d5de-4815-bdf2-fe4b9c9c33b9 · outbound

This paper cites Grayson and Michael E.

Koszul Graded M\"obius Algebras and Strongly Chordal Graphs Grayson and Michael E

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T04:58:50.656276Z

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Observation 99dee7dd-7c3c-4a17-8c50-95a532bd06e6 · outbound

This paper cites Gulliksen.

Koszul Graded M\"obius Algebras and Strongly Chordal Graphs Gulliksen

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T04:58:50.645927Z

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No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation e2381234-6154-4f5e-8b0b-764fbe5a54e9 · outbound

This paper cites Algebra retracts and Poincar´ e-series.

Koszul Graded M\"obius Algebras and Strongly Chordal Graphs Algebra retracts and Poincar´ e-series

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T04:58:50.635789Z

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No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 51466ec8-4d62-4135-a49d-c09c09f8bbb2 · outbound

This paper cites Distributive lattices, aﬃne semigroup rings and algebras with straightening laws.

Koszul Graded M\"obius Algebras and Strongly Chordal Graphs Distributive lattices, aﬃne semigroup rings and algebras with straightening laws

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T04:58:50.625508Z

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No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 27b25934-3ec4-42aa-9a6d-5e5a2b5f6f2e · outbound

This paper cites Enumeration of points, lines, planes, etc.

Koszul Graded M\"obius Algebras and Strongly Chordal Graphs Enumeration of points, lines, planes, etc

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T04:58:50.615097Z

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No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 9fe4fbeb-bf58-42ef-bc6f-ee9b7f8a3984 · outbound

This paper cites Large homomorphisms of local rings.

Koszul Graded M\"obius Algebras and Strongly Chordal Graphs Large homomorphisms of local rings

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T04:58:50.604495Z

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No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 2a1e7054-178a-4c90-910e-ad9a39e9d536 · outbound

This paper cites Chow rings of m atroids are Koszul.

Koszul Graded M\"obius Algebras and Strongly Chordal Graphs Chow rings of m atroids are Koszul

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T04:58:50.593782Z

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No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 8fed554b-0a4b-44af-b9fc-ad83010d0ad2 · outbound

This paper cites Sperner property a nd ﬁnite-dimensional Gorenstein algebras associated to ma troids.

Koszul Graded M\"obius Algebras and Strongly Chordal Graphs Sperner property a nd ﬁnite-dimensional Gorenstein algebras associated to ma troids

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T04:58:50.583632Z

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No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation b6e58509-b299-4d7b-a07c-8eb0a86fe71f · outbound

This paper cites Supersolvable satur ated matroids and chordal graphs.

Koszul Graded M\"obius Algebras and Strongly Chordal Graphs Supersolvable satur ated matroids and chordal graphs

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T04:58:50.572974Z

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No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 18380b02-271e-4013-820e-4a951e61c132 · outbound

This paper cites Qua dratic Gorenstein rings and the Koszul property I.

Koszul Graded M\"obius Algebras and Strongly Chordal Graphs Qua dratic Gorenstein rings and the Koszul property I

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T04:58:50.562955Z

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No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation fcbdf060-a176-4648-9295-24b1521c9841 · outbound

This paper cites Koszul bipartite gr aphs.

Koszul Graded M\"obius Algebras and Strongly Chordal Graphs Koszul bipartite gr aphs

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T04:58:50.552838Z

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No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 18114011-afd7-4a2b-8bee-f19b82c7729c · outbound

This paper cites Combinatorics and topology of complements of hyperplanes, Invent.

Koszul Graded M\"obius Algebras and Strongly Chordal Graphs Combinatorics and topology of complements of hyperplanes, Invent

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T04:58:50.542718Z

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Observation 0d3b5b35-a387-439d-9c4a-95ed3dfce7bb · outbound

This paper cites Matroid theory, volume 21 of Oxford Graduate Texts in Mathematics.

Koszul Graded M\"obius Algebras and Strongly Chordal Graphs Matroid theory, volume 21 of Oxford Graduate Texts in Mathematics

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T04:58:50.532536Z

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No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation f39052b0-fd19-4feb-b81e-808c98d58ef7 · outbound

This paper cites Hyperplane arrangements and linear stran ds in resolutions.

Koszul Graded M\"obius Algebras and Strongly Chordal Graphs Hyperplane arrangements and linear stran ds in resolutions

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T04:58:50.521157Z

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No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation f9f3eec7-33d3-46a9-b49a-4a870333e029 · outbound

This paper cites Graded syzygies, volume 14 of Algebra and Applications.

Koszul Graded M\"obius Algebras and Strongly Chordal Graphs Graded syzygies, volume 14 of Algebra and Applications

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T04:58:50.510814Z

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Observation c0f49054-0397-4692-8195-bcc66fd69ccb · outbound

This paper cites Quadratic algebras , volume 37 of University Lecture Series.

Koszul Graded M\"obius Algebras and Strongly Chordal Graphs Quadratic algebras , volume 37 of University Lecture Series

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T04:58:50.500602Z

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Observation 153e61d2-0e86-45ea-a18f-ccc9dc922fa5 · outbound

This paper cites an unresolved cited work.

Koszul Graded M\"obius Algebras and Strongly Chordal Graphs Unresolved cited work

Reference 36

Resolution: unresolved; raw_fallback, observed 2026-08-11T04:58:50.488740Z

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Observation f3ca09c5-3004-47e0-88c4-6020c1c8841a · outbound

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Koszul Graded M\"obius Algebras and Strongly Chordal Graphs Unresolved cited work

Reference 37

Resolution: unresolved; raw_fallback, observed 2026-08-11T04:58:50.478721Z

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Observation e7e4e3f1-9081-4a95-be5f-76e8213a7e2e · outbound

This paper cites On rational K[π, 1]-spaces and Koszul algebras.

Koszul Graded M\"obius Algebras and Strongly Chordal Graphs On rational K[π, 1]-spaces and Koszul algebras

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T04:58:50.468328Z

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No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation d1ffc3c1-aaa2-46c6-b0e6-50ae4b69c3d0 · outbound

This paper cites Commutative non-Koszul algebras havin g a linear resolution of arbitrarily high order.

Koszul Graded M\"obius Algebras and Strongly Chordal Graphs Commutative non-Koszul algebras havin g a linear resolution of arbitrarily high order

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T04:58:50.457425Z

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No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation c79271c1-05b2-4ab5-8f52-a34718df5d51 · outbound

This paper cites The Burnside algebra of a ﬁnite group.

Koszul Graded M\"obius Algebras and Strongly Chordal Graphs The Burnside algebra of a ﬁnite group

Reference 40

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T04:58:50.446865Z

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No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation bc9b6a2d-05ba-4981-b8c9-acb3722b278a · outbound

This paper cites Schenck and Alexander I.

Koszul Graded M\"obius Algebras and Strongly Chordal Graphs Schenck and Alexander I

Reference 41

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T04:58:50.436312Z

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No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation a90c2668-447e-40d8-99d1-147dcd12dc89 · outbound

This paper cites an unresolved cited work.

Koszul Graded M\"obius Algebras and Strongly Chordal Graphs Unresolved cited work

Reference 42

Resolution: unresolved; raw_fallback, observed 2026-08-11T04:58:50.424923Z

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No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation f0087465-a0f2-47d6-9e02-63f832f4ca13 · outbound

This paper cites Koszul algebras fro m graphs and hyperplane arrangements.

Koszul Graded M\"obius Algebras and Strongly Chordal Graphs Koszul algebras fro m graphs and hyperplane arrangements

Reference 43

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T04:58:50.413193Z

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No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 43ad4333-e64e-4674-a61a-1c88a00cc8eb · outbound

This paper cites MAT-free graphic arran gements and a characterization of strongly chordal graphs b y edge-labeling.

Koszul Graded M\"obius Algebras and Strongly Chordal Graphs MAT-free graphic arran gements and a characterization of strongly chordal graphs b y edge-labeling

Reference 44

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T04:58:50.401963Z

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No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation aeb2ecb3-3ff1-4aed-8ad5-370ee73f822e · outbound

This paper cites an unresolved cited work.

Koszul Graded M\"obius Algebras and Strongly Chordal Graphs Unresolved cited work

Reference 45

Resolution: unresolved; raw_fallback, observed 2026-08-11T04:58:50.389690Z

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No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 3447b3d1-ee5b-4239-9c6a-9f6719ffc5e9 · outbound

This paper cites an unresolved cited work.

Koszul Graded M\"obius Algebras and Strongly Chordal Graphs Unresolved cited work

Reference 46

Resolution: unresolved; raw_fallback, observed 2026-08-11T04:58:50.378863Z

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No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation e2431eb5-bf84-4840-840d-4ff0634f70ad · outbound

This paper cites Yuzvinsky.

Koszul Graded M\"obius Algebras and Strongly Chordal Graphs Yuzvinsky

Reference 47

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T04:58:50.367265Z

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No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Pith citing papers

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