Paper Citation Record · LEDGER

Asymptotically Smaller Encodings for Graph Problems and Scheduling

As of 21 August 2026, this Paper Citation Record lists 37 of 37 outbound references and 1 inbound Pith citation observation for arXiv:2506.14042.

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

pith.paper-citation-record.v1
2506.14042 v1

Coverage vector

measured 37 of 37 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-15T20:12:18.107887Z

measured 38 of 38 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-21T06:32:19.484+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-05-14T21:40:47.491357Z

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: arxiv_reference, observed 2026-05-14T21:43:00.724783Z

Reference resolution

37 of 37 outbound references displayed

verified exact12
verified fuzzy10
unresolved13
parse uncertain0
malformed identifier0
metadata mismatch2

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 3b55024a-f557-48b6-b377-27b48e7fd264 · outbound

This paper cites Covering graphs by the minimum number of equivalence relations.

Asymptotically Smaller Encodings for Graph Problems and Scheduling Covering graphs by the minimum number of equivalence relations

Reference 1

Resolution: verified exact; doi, observed 2026-08-15T20:12:18.391072Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 832366cb-eb5c-46ea-83a5-b96b9f9aa38c · outbound

This paper cites Cardinality Networks : A theoretical and empirical study.

Asymptotically Smaller Encodings for Graph Problems and Scheduling Cardinality Networks : A theoretical and empirical study

Reference 2

Resolution: verified exact; doi, observed 2026-08-15T20:12:18.372597Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 41707ed6-c1f1-432b-ba9e-e4b4832081fb · outbound

This paper cites Computing NP-Hard Repetitiveness Measures via MAX-SAT.

Asymptotically Smaller Encodings for Graph Problems and Scheduling Computing NP-Hard Repetitiveness Measures via MAX-SAT

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-15T20:12:17.919945Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 57fcefe0-30de-4027-adb4-fb12fdfc2bf2 · outbound

This paper cites Computing NP-Hard Repetitiveness Measures via MAX-SAT (under review), 2025.

Asymptotically Smaller Encodings for Graph Problems and Scheduling Computing NP-Hard Repetitiveness Measures via MAX-SAT (under review), 2025

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:12:18.978513Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation afc64521-7d33-4e1f-b1d0-f0734a077199 · outbound

This paper cites exactly one clauses · I ssue \#39 · arminbiere/kissat --- github.com.

Asymptotically Smaller Encodings for Graph Problems and Scheduling exactly one clauses · I ssue \#39 · arminbiere/kissat --- github.com

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:12:18.958349Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation f9218af0-cb67-43ff-a548-bd92d9fed14d · outbound

This paper cites Successful SAT encoding techniques.

Asymptotically Smaller Encodings for Graph Problems and Scheduling Successful SAT encoding techniques

Reference 6

Resolution: verified exact; doi, observed 2026-08-15T20:12:18.354456Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 3165e823-1eba-4960-a616-e6d2a1dc16e9 · outbound

This paper cites A new sat encoding of the at-most-one constraint.

Asymptotically Smaller Encodings for Graph Problems and Scheduling A new sat encoding of the at-most-one constraint

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:12:18.939187Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 001cf94c-085e-48e7-ab25-5e0284b21929 · outbound

This paper cites o zy, editors, Studies in Pure Mathematics : To the Memory of Paul Tur \'a n , pages 95--101. Birkh \.

Asymptotically Smaller Encodings for Graph Problems and Scheduling o zy, editors, Studies in Pure Mathematics : To the Memory of Paul Tur \'a n , pages 95--101. Birkh \

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-15T20:12:17.948722Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 093ded1d-17c3-4fef-8321-578e796fcd9a · outbound

This paper cites Clique covering of large real-world networks.

Asymptotically Smaller Encodings for Graph Problems and Scheduling Clique covering of large real-world networks

Reference 9

Resolution: metadata mismatch; raw_fallback, observed 2026-08-15T20:12:18.738122Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation a82d16e1-7022-4bd2-a678-4eeece8940ba · outbound

This paper cites On the Decomposition of Graphs into Complete Bipartite Graphs.

Asymptotically Smaller Encodings for Graph Problems and Scheduling On the Decomposition of Graphs into Complete Bipartite Graphs

Reference 10

Resolution: verified exact; doi, observed 2026-08-15T20:12:18.325421Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation bf28625c-7536-4d1e-a401-f5dfa11fc927 · outbound

This paper cites Kulikov, Ivan Mihajlin, and Nikita Slezkin.

Asymptotically Smaller Encodings for Graph Problems and Scheduling Kulikov, Ivan Mihajlin, and Nikita Slezkin

Reference 11

Resolution: verified exact; doi, observed 2026-08-15T20:12:18.306674Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 7a07df06-c3c6-4c66-b059-776b01a8f486 · outbound

This paper cites Fishburn and Peter L.

Asymptotically Smaller Encodings for Graph Problems and Scheduling Fishburn and Peter L

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-15T20:12:17.971952Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d2e26f59-b48e-4219-96f1-33f5bb0d477b · outbound

This paper cites Covering the edges of a random graph by cliques.

Asymptotically Smaller Encodings for Graph Problems and Scheduling Covering the edges of a random graph by cliques

Reference 13

Resolution: verified exact; doi, observed 2026-08-15T20:12:18.276645Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation ac1b2175-fbe8-431a-b104-ebe213b0edcc · outbound

This paper cites Covering the edges of a random graph by cliques.

Asymptotically Smaller Encodings for Graph Problems and Scheduling Covering the edges of a random graph by cliques

Reference 14

Resolution: verified exact; local_arxiv, observed 2026-08-15T20:12:18.656735Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation ddca5b7e-5a56-4585-bdd3-a02bf8b1c9c9 · outbound

This paper cites an unresolved cited work.

Asymptotically Smaller Encodings for Graph Problems and Scheduling Unresolved cited work

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-15T20:12:17.987621Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 24464f83-4023-4845-bbfc-43d07367375e · outbound

This paper cites an unresolved cited work.

Asymptotically Smaller Encodings for Graph Problems and Scheduling Unresolved cited work

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-15T20:12:17.993353Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 776a831e-c572-4b6b-9f01-ea72ecbf2059 · outbound

This paper cites an unresolved cited work.

Asymptotically Smaller Encodings for Graph Problems and Scheduling Unresolved cited work

Reference 17

Resolution: verified exact; doi, observed 2026-08-15T20:12:18.235650Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation a580d387-61bd-465b-96ba-209a608e26ea · outbound

This paper cites Is the smallest grammar problem over the singleton alphabet known to be np-complete or ...? Computer Science Stack Exchange, 2025.

Asymptotically Smaller Encodings for Graph Problems and Scheduling Is the smallest grammar problem over the singleton alphabet known to be np-complete or ...? Computer Science Stack Exchange, 2025

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:12:18.919248Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 7e1e2a41-0bd7-4ae6-941f-2f66970baea8 · outbound

This paper cites Cardinality encodings for graph optimization problems.

Asymptotically Smaller Encodings for Graph Problems and Scheduling Cardinality encodings for graph optimization problems

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:12:18.900518Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 8046e2f8-e294-424b-b26c-00c9324ca506 · outbound

This paper cites Computational Complexity of Graphs.

Asymptotically Smaller Encodings for Graph Problems and Scheduling Computational Complexity of Graphs

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-15T20:12:18.017368Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 33bd71e6-fae3-4440-9a4e-054d7cb1f5b8 · outbound

This paper cites A lower bound on CNF encodings of the at-most-one constraint.

Asymptotically Smaller Encodings for Graph Problems and Scheduling A lower bound on CNF encodings of the at-most-one constraint

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-15T20:12:18.023242Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7c308426-9950-4db9-9959-3d46efd1109e · outbound

This paper cites an unresolved cited work.

Asymptotically Smaller Encodings for Graph Problems and Scheduling Unresolved cited work

Reference 22

Resolution: unresolved; raw_fallback, observed 2026-08-15T20:12:18.879295Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation ff35df8c-93a0-4e32-98c6-f66c635f6601 · outbound

This paper cites Timetabling based on sat encoding: a case study.

Asymptotically Smaller Encodings for Graph Problems and Scheduling Timetabling based on sat encoding: a case study

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:12:18.861512Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 1f33bdcd-7a3f-4e6e-a105-59f88cd92d49 · outbound

This paper cites Efficient SAT encoding scheme for schedulability analysis of non-preemptive tasks on multiple computational resources.

Asymptotically Smaller Encodings for Graph Problems and Scheduling Efficient SAT encoding scheme for schedulability analysis of non-preemptive tasks on multiple computational resources

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-15T20:12:18.038927Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7442533a-1eb4-477b-ac38-ad0835f619a5 · outbound

This paper cites Finding bipartite subgraphs efficiently.

Asymptotically Smaller Encodings for Graph Problems and Scheduling Finding bipartite subgraphs efficiently

Reference 25

Resolution: verified exact; doi, observed 2026-08-15T20:12:18.197088Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 76513c6c-a266-49c1-8b5e-e7a990221ecd · outbound

This paper cites Empirical study on sat-encodings of the at-most-one constraint.

Asymptotically Smaller Encodings for Graph Problems and Scheduling Empirical study on sat-encodings of the at-most-one constraint

Reference 26

Resolution: metadata mismatch; raw_fallback, observed 2026-08-15T20:12:18.561957Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 65d14dd0-bd33-4c6b-a187-4ce6a49b8a17 · outbound

This paper cites C liquer homepage --- users.aalto.fi.

Asymptotically Smaller Encodings for Graph Problems and Scheduling C liquer homepage --- users.aalto.fi

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:12:18.843671Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation b16ac632-5a86-4a04-b6d1-c36e601e8531 · outbound

This paper cites CNF Encodings, chapter 2.

Asymptotically Smaller Encodings for Graph Problems and Scheduling CNF Encodings, chapter 2

Reference 28

Resolution: verified exact; doi, observed 2026-08-15T20:12:18.176608Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 8afc2813-44dd-4030-9c26-87a0016f221a · outbound

This paper cites Unfolding Boxes with Local Constraints.

Asymptotically Smaller Encodings for Graph Problems and Scheduling Unfolding Boxes with Local Constraints

Reference 29

Resolution: verified exact; local_arxiv, observed 2026-08-15T20:12:18.446915Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 4437be84-d2bb-4fe1-be6b-32da490c255a · outbound

This paper cites Compact representation of sets of binary constraints.

Asymptotically Smaller Encodings for Graph Problems and Scheduling Compact representation of sets of binary constraints

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:12:18.826933Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation a96b46c2-6474-4297-a754-ee14525e1799 · outbound

This paper cites SAT-based Decision Tree Learning for Large Data Sets.

Asymptotically Smaller Encodings for Graph Problems and Scheduling SAT-based Decision Tree Learning for Large Data Sets

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-15T20:12:18.075961Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3785f0cd-0e9c-4eb7-8280-f9c27e5cdeb1 · outbound

This paper cites Towards an Optimal CNF Encoding of Boolean Cardinality Constraints.

Asymptotically Smaller Encodings for Graph Problems and Scheduling Towards an Optimal CNF Encoding of Boolean Cardinality Constraints

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:12:18.807285Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation cd39fce0-1547-44f5-84ef-3bd70898ea59 · outbound

This paper cites an unresolved cited work.

Asymptotically Smaller Encodings for Graph Problems and Scheduling Unresolved cited work

Reference 33

Resolution: unresolved; no resolver link, observed 2026-08-15T20:12:18.087768Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3264402b-d0fd-483e-8d63-9d696564cc20 · outbound

This paper cites The Packing Chromatic Number of the Infinite Square Grid Is at Least 14.

Asymptotically Smaller Encodings for Graph Problems and Scheduling The Packing Chromatic Number of the Infinite Square Grid Is at Least 14

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:12:18.776179Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation ef5ecd23-350b-4f19-87bf-3268dadcd92e · outbound

This paper cites an unresolved cited work.

Asymptotically Smaller Encodings for Graph Problems and Scheduling Unresolved cited work

Reference 35

Resolution: unresolved; raw_fallback, observed 2026-08-15T20:12:18.757957Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation f37bb63f-385a-4b89-9f18-bbc938fd9137 · outbound

This paper cites A review on algorithms for maximum clique problems.

Asymptotically Smaller Encodings for Graph Problems and Scheduling A review on algorithms for maximum clique problems

Reference 36

Resolution: unresolved; no resolver link, observed 2026-08-15T20:12:18.102840Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fc38e807-dc48-43e0-9485-e9884bd14262 · outbound

This paper cites Yet Another Comparison of SAT Encodings for the At-Most-K Constraint.

Asymptotically Smaller Encodings for Graph Problems and Scheduling Yet Another Comparison of SAT Encodings for the At-Most-K Constraint

Reference 37

Resolution: verified exact; local_arxiv, observed 2026-08-15T20:12:18.419788Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Pith citing papers

Observation 4763e0c3-465d-468b-8920-70ed30d637ed · inbound

Automated Reencoding Meets Graph Theory cites this paper.

Automated Reencoding Meets Graph Theory Asymptotically Smaller Encodings for Graph Problems and Scheduling

Reference 24

Resolution: verified exact; arxiv_id, observed 2026-05-14T21:43:00.726700Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.