Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-07T14:44:00.114160Z
Paper Citation Record · LEDGER
On the geometric $k$-colored crossing number of $K_n$
As of 16 August 2026, this Paper Citation Record lists 25 of 25 outbound references and 0 inbound Pith citation observations for arXiv:2505.18014.
A citation records a reference. It does not transfer a finding from one paper to another.
Coverage vector
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-16T06:30:59.297886+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links
A source-named dated measurement, never combined with another source.
Source: cited_works
Reference resolution
25 of 25 outbound references displayed
- verified exact10
- verified fuzzy4
- unresolved7
- parse uncertain0
- malformed identifier3
- metadata mismatch1
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation bf6246e7-5c00-4415-b87b-2e8e37b4c9ed · outbound
This paper cites On ≤ k-Edges, Crossings, and Halving Lines of Geometric Drawings of Kn.
On the geometric $k$-colored crossing number of $K_n$ On ≤ k-Edges, Crossings, and Halving Lines of Geometric Drawings of Kn
Reference 1
- Resolution
- verified exact
- doi, observed 2026-08-07T14:44:02.065049Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 5f933d9a-6f47-4c03-8144-130f8c8b76c6 · outbound
This paper cites Geometric Drawings ofKn with Few Crossings.
On the geometric $k$-colored crossing number of $K_n$ Geometric Drawings ofKn with Few Crossings
Reference 2
- Resolution
- verified exact
- doi, observed 2026-08-07T14:44:01.794844Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 1665a07b-5e93-4fc8-aac5-d91f1fdf451c · outbound
This paper cites On Topological Graphs with at Most Four Crossings per Edge.
On the geometric $k$-colored crossing number of $K_n$ On Topological Graphs with at Most Four Crossings per Edge
Reference 3
- Resolution
- unresolved
- no resolver link, observed 2026-08-07T14:43:57.876099Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation db47ff55-6b82-4977-a6b2-2234fd29edb4 · outbound
This paper cites An Ongoing Project to Improve the Rectilinear and the Pseudolinear Crossing Constants.
On the geometric $k$-colored crossing number of $K_n$ An Ongoing Project to Improve the Rectilinear and the Pseudolinear Crossing Constants
Reference 4
- Resolution
- verified exact
- local_arxiv, observed 2026-08-07T14:44:02.956485Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation b3b9dbc8-bb26-4288-acf2-56c114a51a24 · outbound
This paper cites On the 2-Colored Crossing Number.
On the geometric $k$-colored crossing number of $K_n$ On the 2-Colored Crossing Number
Reference 5
- Resolution
- verified exact
- doi, observed 2026-08-07T14:44:01.587443Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation d2b49c22-10ee-4c5e-9e24-c3b6833ab178 · outbound
This paper cites New Lower Bounds for the Number of (≤ k)-Edges and the Rectilinear Crossing Number of Kn.
On the geometric $k$-colored crossing number of $K_n$ New Lower Bounds for the Number of (≤ k)-Edges and the Rectilinear Crossing Number of Kn
Reference 6
- Resolution
- verified exact
- doi, observed 2026-08-07T14:44:01.340041Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 6832c792-32f9-4155-9eae-4c040d8afaed · outbound
This paper cites Polynomial Time Approximation Schemes for Dense Instances of N P-Hard Problems.
On the geometric $k$-colored crossing number of $K_n$ Polynomial Time Approximation Schemes for Dense Instances of N P-Hard Problems
Reference 7
- Resolution
- unresolved
- no resolver link, observed 2026-08-07T14:43:58.309585Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation e8a57e96-8c5c-4e01-815a-eda2c470d8f4 · outbound
This paper cites Some Provably Hard Crossing Number Problems.
On the geometric $k$-colored crossing number of $K_n$ Some Provably Hard Crossing Number Problems
Reference 8
- Resolution
- unresolved
- no resolver link, observed 2026-08-07T14:43:58.427075Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 81dc7717-7a0c-4d87-9ba9-44dd241b5c72 · outbound
This paper cites A Note on the 2-Colored Rectilinear Crossing Number of Random Point Sets in the Unit Square.
On the geometric $k$-colored crossing number of $K_n$ A Note on the 2-Colored Rectilinear Crossing Number of Random Point Sets in the Unit Square
Reference 9
- Resolution
- verified exact
- doi, observed 2026-08-07T14:44:01.149989Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation b847f34c-3f9d-4092-8873-00d9a032f97f · outbound
This paper cites An Upper Bound to the Crossing Number of the Complete Graph Drawn on the Pages of a Book.
On the geometric $k$-colored crossing number of $K_n$ An Upper Bound to the Crossing Number of the Complete Graph Drawn on the Pages of a Book
Reference 10
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T14:44:04.125227Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation c5bba66c-66d6-42f5-85a3-169bee8f4e32 · outbound
This paper cites Improved Lower Bounds on Book Crossing Numbers of Complete Graphs.
On the geometric $k$-colored crossing number of $K_n$ Improved Lower Bounds on Book Crossing Numbers of Complete Graphs
Reference 11
- Resolution
- verified exact
- doi, observed 2026-08-07T14:44:00.924333Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation f9c4fc7a-f205-4ef4-8eb2-ee04e69f6e7f · outbound
This paper cites Mathematical Programming Formulation of Rectilinear Crossing Minimization.
On the geometric $k$-colored crossing number of $K_n$ Mathematical Programming Formulation of Rectilinear Crossing Minimization
Reference 12
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T14:44:03.886434Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 438f6946-aa82-475c-b696-98d5c0dcfc74 · outbound
This paper cites A Note on the k -Colored Crossing Ratio of Dense Geometric Graphs.
On the geometric $k$-colored crossing number of $K_n$ A Note on the k -Colored Crossing Ratio of Dense Geometric Graphs
Reference 13
- Resolution
- metadata mismatch
- raw_fallback, observed 2026-08-07T14:44:02.670861Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 6394758c-fefd-4a71-8947-8f4447eaad8f · outbound
This paper cites Some Simplified NP -Complete Graph Problems.
On the geometric $k$-colored crossing number of $K_n$ Some Simplified NP -Complete Graph Problems
Reference 14
- Resolution
- malformed identifier
- no resolver link, observed 2026-08-07T14:43:59.017456Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation cab591f5-8348-43e3-90ce-b1d3659cbf88 · outbound
This paper cites Instances with Low Geometric k-Colored Crossing Number.
On the geometric $k$-colored crossing number of $K_n$ Instances with Low Geometric k-Colored Crossing Number
Reference 15
- Resolution
- verified exact
- doi, observed 2026-08-07T14:44:00.741627Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 16f8bf94-845c-47f6-bd2f-0a20d8054b11 · outbound
This paper cites On the Hardness of Approximating Max k -Cut and Its Dual.
On the geometric $k$-colored crossing number of $K_n$ On the Hardness of Approximating Max k -Cut and Its Dual
Reference 16
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T14:44:03.671140Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation b816ea6b-0c66-4b27-8361-a3672e0e12e8 · outbound
This paper cites The Hungarian Method for the Assignment Problem.
On the geometric $k$-colored crossing number of $K_n$ The Hungarian Method for the Assignment Problem
Reference 17
- Resolution
- unresolved
- no resolver link, observed 2026-08-07T14:43:59.281722Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 150b57f1-5a79-454a-8d45-0a6db3a6df94 · outbound
This paper cites Crossing Minimization in Linear Embeddings of Graphs.
On the geometric $k$-colored crossing number of $K_n$ Crossing Minimization in Linear Embeddings of Graphs
Reference 18
- Resolution
- verified exact
- doi, observed 2026-08-07T14:44:00.548582Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation be83c4ad-1681-4f0c-a15e-927d3aeaec69 · outbound
This paper cites Note onk -Planar Crossing Numbers.
On the geometric $k$-colored crossing number of $K_n$ Note onk -Planar Crossing Numbers
Reference 19
- Resolution
- verified exact
- doi, observed 2026-08-07T14:44:00.325682Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation a7a56ecf-083b-4a65-9626-f0f76ebc27ab · outbound
This paper cites Relations Between Crossing Numbers of Complete and Complete Bipartite Graphs.
On the geometric $k$-colored crossing number of $K_n$ Relations Between Crossing Numbers of Complete and Complete Bipartite Graphs
Reference 20
- Resolution
- unresolved
- no resolver link, observed 2026-08-07T14:43:59.614110Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 1748a9d1-979d-4fc9-83a3-79d0e3c68800 · outbound
This paper cites an unresolved cited work.
On the geometric $k$-colored crossing number of $K_n$ Unresolved cited work
Reference 21
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T14:44:03.405535Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 207361e0-4904-4162-bfba-1036b24abcc6 · outbound
This paper cites Computational Study of a Branching Algorithm for the Maximum k -Cut Problem.
On the geometric $k$-colored crossing number of $K_n$ Computational Study of a Branching Algorithm for the Maximum k -Cut Problem
Reference 22
- Resolution
- unresolved
- no resolver link, observed 2026-08-07T14:43:59.821797Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation ba8f03f5-faa8-4dfb-a168-aecc53c647a3 · outbound
This paper cites The Graph Crossing Number and Its Variants: A Survey.
On the geometric $k$-colored crossing number of $K_n$ The Graph Crossing Number and Its Variants: A Survey
Reference 23
- Resolution
- malformed identifier
- no resolver link, observed 2026-08-07T14:43:59.927904Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 2712d596-4e7c-4573-8e7d-167e668ba8a0 · outbound
This paper cites The Book Crossing Number of a Graph.
On the geometric $k$-colored crossing number of $K_n$ The Book Crossing Number of a Graph
Reference 24
- Resolution
- malformed identifier
- no resolver link, observed 2026-08-07T14:44:00.027770Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation cffd4f08-e110-4796-ab06-a2348e8ac8be · outbound
This paper cites On the Biplanar and k-Planar Crossing Numbers.
On the geometric $k$-colored crossing number of $K_n$ On the Biplanar and k-Planar Crossing Numbers
Reference 25
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T14:44:03.202827Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Pith citing papers
No inbound Pith citation observations are available.