Paper Citation Record · LEDGER

Rectangular Duals on the Cylinder and the Torus

As of 9 August 2026, this Paper Citation Record lists 47 of 47 outbound references and 0 inbound Pith citation observations for arXiv:2506.07170.

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

pith.paper-citation-record.v1
2506.07170 v1

Coverage vector

measured 47 of 47 reference resolution

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Source: paper_references, paper_reference_links, observed 2026-08-07T05:48:12.604412Z

measured 47 of 47 standing notices

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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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Reference resolution

47 of 47 outbound references displayed

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verified fuzzy4
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External citation measurements

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Outbound references

Observation ca0f3977-9a06-4fbb-b95f-b0813c3bd8f9 · outbound

This paper cites Kobourov, Sergey Pupyrev, André Schulz, and Torsten Ueckerdt.

Rectangular Duals on the Cylinder and the Torus Kobourov, Sergey Pupyrev, André Schulz, and Torsten Ueckerdt

Reference 1

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Observation cb7848e6-9250-4167-9d81-1f8ac894794e · outbound

This paper cites Beyondlevelplanarity: Cyclic, torus, andsimultaneouslevelplanarity.

Rectangular Duals on the Cylinder and the Torus Beyondlevelplanarity: Cyclic, torus, andsimultaneouslevelplanarity

Reference 2

Resolution: verified exact; doi, observed 2026-08-07T05:48:13.120074Z

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Observation e8ea5291-502e-4ea3-8869-8544fdde8684 · outbound

This paper cites Grand-schnyder woods.Annals of Combina- torics, 2024.doi:10.1007/s00026-024-00729-8.

Rectangular Duals on the Cylinder and the Torus Grand-schnyder woods.Annals of Combina- torics, 2024.doi:10.1007/s00026-024-00729-8

Reference 3

Resolution: verified exact; doi, observed 2026-08-07T05:48:13.105033Z

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Observation 68ab6625-a21a-401d-843f-215faaca174c · outbound

This paper cites A linear time algorithm to check for the existence of a rectangular dual of a planar triangulated graph.Networks, 17(3):307–317, 1987.doi: 10.1002/net.3230170306.

Rectangular Duals on the Cylinder and the Torus A linear time algorithm to check for the existence of a rectangular dual of a planar triangulated graph.Networks, 17(3):307–317, 1987.doi: 10.1002/net.3230170306

Reference 4

Resolution: verified exact; doi, observed 2026-08-07T05:48:13.089708Z

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Observation 1130a5a3-214b-40ce-89b7-90987c747d10 · outbound

This paper cites Visibility representations of toroidal and Klein-bottle graphs.

Rectangular Duals on the Cylinder and the Torus Visibility representations of toroidal and Klein-bottle graphs

Reference 5

Resolution: verified exact; doi, observed 2026-08-07T05:48:13.073859Z

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Observation b97e440b-c1a1-4624-9cd6-91ddc5be05a6 · outbound

This paper cites The (3,1)-ordering for 4-connected planar triangulations.

Rectangular Duals on the Cylinder and the Torus The (3,1)-ordering for 4-connected planar triangulations

Reference 6

Resolution: malformed identifier; no resolver link, observed 2026-08-07T05:48:12.418983Z

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Observation f07e9488-f810-4173-a29d-31e22d34b057 · outbound

This paper cites A bijection for essentially 4-connected toroidal triangulations.Electronic Journal of Combinatorics, 26(1):1, 2019.doi:10.37236/7897.

Rectangular Duals on the Cylinder and the Torus A bijection for essentially 4-connected toroidal triangulations.Electronic Journal of Combinatorics, 26(1):1, 2019.doi:10.37236/7897

Reference 7

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Observation a9d7bdb7-678d-4a19-90fd-3b4449b3153f · outbound

This paper cites Buchsbaum, Emden R.

Rectangular Duals on the Cylinder and the Torus Buchsbaum, Emden R

Reference 8

Resolution: metadata mismatch; raw_fallback, observed 2026-08-07T05:48:13.466476Z

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Observation acc48730-7c49-46a8-87da-a408b5b669f0 · outbound

This paper cites Canonical ordering for triangulations on the cylinder, with applications to periodic straight-line drawings.

Rectangular Duals on the Cylinder and the Torus Canonical ordering for triangulations on the cylinder, with applications to periodic straight-line drawings

Reference 9

Resolution: verified exact; doi, observed 2026-08-07T05:48:13.033365Z

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Observation d67de240-7e11-43b6-b8ca-f2fc91fe0175 · outbound

This paper cites Drawinggraphs in the plane with a prescribed outer face and polynomial area.

Rectangular Duals on the Cylinder and the Torus Drawinggraphs in the plane with a prescribed outer face and polynomial area

Reference 10

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Observation 509a2a6d-f5bd-4cb1-83fb-066a739c88bf · outbound

This paper cites How to morph graphs on thetorus.

Rectangular Duals on the Cylinder and the Torus How to morph graphs on thetorus

Reference 11

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Observation f4fad8df-359b-40b9-be98-ae77459b17bd · outbound

This paper cites Detecting weakly simple polygons.

Rectangular Duals on the Cylinder and the Torus Detecting weakly simple polygons

Reference 12

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Observation 215f3fe0-6c7c-4d69-b17d-4c5bb7f7330b · outbound

This paper cites Simple algorithms for partial and simultaneous rectangular duals with given contact orientations.Theoretical Computer Science, 919:66–74, 2022.doi:10.1016/j.tcs.

Rectangular Duals on the Cylinder and the Torus Simple algorithms for partial and simultaneous rectangular duals with given contact orientations.Theoretical Computer Science, 919:66–74, 2022.doi:10.1016/j.tcs

Reference 13

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Observation 78618f5f-15c7-445b-83e0-a4a59820bb5e · outbound

This paper cites Morphing rectangular duals.

Rectangular Duals on the Cylinder and the Torus Morphing rectangular duals

Reference 14

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Observation 45e2ff0c-72f3-4297-a41d-616064772f4f · outbound

This paper cites DoughNets: visualising networks using torus wrapping.

Rectangular Duals on the Cylinder and the Torus DoughNets: visualising networks using torus wrapping

Reference 15

Resolution: malformed identifier; no resolver link, observed 2026-08-07T05:48:12.461154Z

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Observation 8ca8f2b0-4d51-4f30-bb06-2a3edd2f2dd2 · outbound

This paper cites Devanny, David Eppstein, and Timothy Johnson.

Rectangular Duals on the Cylinder and the Torus Devanny, David Eppstein, and Timothy Johnson

Reference 16

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Observation b4c9082c-9bda-4ced-bd61-a8e421fcd854 · outbound

This paper cites On triangle con- tact graphs.Combinatorics, Probability and Computing, 3(2):233–246, 1994.doi:10.1017/ S0963548300001139.

Rectangular Duals on the Cylinder and the Torus On triangle con- tact graphs.Combinatorics, Probability and Computing, 3(2):233–246, 1994.doi:10.1017/ S0963548300001139

Reference 17

Resolution: malformed identifier; raw_fallback, observed 2026-08-07T05:48:13.577394Z

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Observation d1a5532e-bdcd-48ff-b88a-c989743e8b96 · outbound

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Rectangular Duals on the Cylinder and the Torus Unresolved cited work

Reference 18

Resolution: verified exact; doi, observed 2026-08-07T05:48:12.945792Z

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Observation a515f89d-9b13-41e5-8cfd-aff82594f619 · outbound

This paper cites Duncan, Michael T.

Rectangular Duals on the Cylinder and the Torus Duncan, Michael T

Reference 19

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Observation 7238b27a-0e2b-427a-b301-86a0867d2d17 · outbound

This paper cites Triangle-free penny graphs: Degeneracy, choosability, and edge count.

Rectangular Duals on the Cylinder and the Torus Triangle-free penny graphs: Degeneracy, choosability, and edge count

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-07T05:48:12.483231Z

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Observation b288c09f-a5f4-4199-885c-5e146335ea48 · outbound

This paper cites Area-universal and constrained rectangular layouts.SIAM Journal on Computing, 41(3):537–564, 2012.doi: 10.1137/110834032.

Rectangular Duals on the Cylinder and the Torus Area-universal and constrained rectangular layouts.SIAM Journal on Computing, 41(3):537–564, 2012.doi: 10.1137/110834032

Reference 21

Resolution: verified exact; doi, observed 2026-08-07T05:48:12.906911Z

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Observation dd71f25e-b0ed-4b06-aa00-fce0a5c5e745 · outbound

This paper cites Planar and toroidal morphs made easier.Journal of Graph Algorithms and Applications, 27(2):95–118, 2023.doi:10.7155/jgaa.00616.

Rectangular Duals on the Cylinder and the Torus Planar and toroidal morphs made easier.Journal of Graph Algorithms and Applications, 27(2):95–118, 2023.doi:10.7155/jgaa.00616

Reference 22

Resolution: verified exact; doi, observed 2026-08-07T05:48:12.891175Z

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Observation 851f90eb-9cd7-4647-ad79-31b1e694b96c · outbound

This paper cites Transversal structures on triangulations: A combinatorial study and straight-line drawings.Discrete Mathematics, 309(7):1870–1894, 2009.doi:10.1016/j.disc.2007.12.

Rectangular Duals on the Cylinder and the Torus Transversal structures on triangulations: A combinatorial study and straight-line drawings.Discrete Mathematics, 309(7):1870–1894, 2009.doi:10.1016/j.disc.2007.12

Reference 23

Resolution: verified exact; doi, observed 2026-08-07T05:48:12.875739Z

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Observation 7fd02aea-9b01-43dc-b578-05fd87f15ad2 · outbound

This paper cites Ruben Gabriel and Robert R.

Rectangular Duals on the Cylinder and the Torus Ruben Gabriel and Robert R

Reference 24

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Observation 0288d836-7f01-4a78-a62d-7e3b0f12f4ab · outbound

This paper cites Toroidalmaps: Schnyderwoods, orthogonalsurfaces and straight-line representations.Discrete & Computational Geometry, 51(1):67–131, 2014.

Rectangular Duals on the Cylinder and the Torus Toroidalmaps: Schnyderwoods, orthogonalsurfaces and straight-line representations.Discrete & Computational Geometry, 51(1):67–131, 2014

Reference 25

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Observation ecf44678-3c8b-49a7-bf3c-3ac07c453125 · outbound

This paper cites On finding the rectangular duals of planar triangular graphs.SIAM Journal on Computing, 22(6):1218–1226, 1993.doi:10.1137/0222072.

Rectangular Duals on the Cylinder and the Torus On finding the rectangular duals of planar triangular graphs.SIAM Journal on Computing, 22(6):1218–1226, 1993.doi:10.1137/0222072

Reference 26

Resolution: verified exact; doi, observed 2026-08-07T05:48:12.833815Z

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Observation f87712e8-bea2-47a5-a032-a8bedbf46e17 · outbound

This paper cites Contact graphs of line segments are np-complete.Discrete Mathematics, 235(1- 3):95–106, 2001.doi:10.1016/S0012-365X(00)00263-6.

Rectangular Duals on the Cylinder and the Torus Contact graphs of line segments are np-complete.Discrete Mathematics, 235(1- 3):95–106, 2001.doi:10.1016/S0012-365X(00)00263-6

Reference 27

Resolution: verified exact; doi, observed 2026-08-07T05:48:12.818652Z

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Observation 5c682d3e-259c-4ae8-a783-d0a2dfc84f8f · outbound

This paper cites Representing graphs by disks and balls (a survey of recognition-complexityresults).Discrete Mathematics, 229(1-3):101–124, 2001.doi:10.1016/ S0012-365X(00)00204-1.

Rectangular Duals on the Cylinder and the Torus Representing graphs by disks and balls (a survey of recognition-complexityresults).Discrete Mathematics, 229(1-3):101–124, 2001.doi:10.1016/ S0012-365X(00)00204-1

Reference 28

Resolution: malformed identifier; raw_fallback, observed 2026-08-07T05:48:13.561940Z

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Observation ae56ce3f-163a-4186-87b4-6de44e5f9274 · outbound

This paper cites Regular edge labeling of 4-connected plane graphs and its applications in graph drawing problems.Theoretical Computer Science, 172(1):175–193, 1997.doi:10.

Rectangular Duals on the Cylinder and the Torus Regular edge labeling of 4-connected plane graphs and its applications in graph drawing problems.Theoretical Computer Science, 172(1):175–193, 1997.doi:10

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:48:13.546126Z

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Observation 1da10eb4-9c55-4fa4-9471-3528d232ef18 · outbound

This paper cites Combinatorial properties of triangle-free rectangle arrangements and the squarability problem.

Rectangular Duals on the Cylinder and the Torus Combinatorial properties of triangle-free rectangle arrangements and the squarability problem

Reference 30

Resolution: verified exact; doi, observed 2026-08-07T05:48:12.800792Z

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Observation c85eba00-60b7-492c-a784-7f076519bbc9 · outbound

This paper cites Kontaktprobleme der konformen Abbildung.Berichte über die Verhandlungen der Sächsischen Akademie der Wiss.

Rectangular Duals on the Cylinder and the Torus Kontaktprobleme der konformen Abbildung.Berichte über die Verhandlungen der Sächsischen Akademie der Wiss

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:48:13.529270Z

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Observation 443cd25c-db5a-431e-be2d-38d045914559 · outbound

This paper cites Rectangular duals of planar graphs.Networks, 15(2):145–157, 1985.doi:10.1002/net.3230150202.

Rectangular Duals on the Cylinder and the Torus Rectangular duals of planar graphs.Networks, 15(2):145–157, 1985.doi:10.1002/net.3230150202

Reference 32

Resolution: verified exact; doi, observed 2026-08-07T05:48:12.785936Z

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Observation 62285590-aff4-4c26-99c6-c91add77ddde · outbound

This paper cites Grid intersection and box intersection graphs on sur- faces.

Rectangular Duals on the Cylinder and the Torus Grid intersection and box intersection graphs on sur- faces

Reference 33

Resolution: verified exact; doi, observed 2026-08-07T05:48:12.771036Z

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Observation edffcd45-7665-4248-b2bb-b347167fe7f0 · outbound

This paper cites On the characterization of rectangular duals.

Rectangular Duals on the Cylinder and the Torus On the characterization of rectangular duals

Reference 34

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Observation 6f032b72-a1e5-4f3c-8b6c-fcf219989437 · outbound

This paper cites Leinwand.

Rectangular Duals on the Cylinder and the Torus Leinwand

Reference 35

Resolution: verified exact; doi, observed 2026-08-07T05:48:12.755567Z

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Observation 55eccd77-45ee-4217-9983-892a1be3b5bb · outbound

This paper cites Computing a canon- ical polygonal schema of an orientable triangulated surface.

Rectangular Duals on the Cylinder and the Torus Computing a canon- ical polygonal schema of an orientable triangulated surface

Reference 36

Resolution: metadata mismatch; raw_fallback, observed 2026-08-07T05:48:13.318967Z

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Observation e807a02f-ad65-4bae-b4ac-a2b1740eaf88 · outbound

This paper cites Leinwand and Yen-Tai Lai.

Rectangular Duals on the Cylinder and the Torus Leinwand and Yen-Tai Lai

Reference 37

Resolution: metadata mismatch; raw_fallback, observed 2026-08-07T05:48:13.233685Z

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Observation b1661b39-3fc6-4a6a-9ed7-5feeb979f95b · outbound

This paper cites Tessellation and visibility representations of maps on the torus.Discrete & Computational Geometry, 19:249–263, 1998.doi:10.1007/PL00009344.

Rectangular Duals on the Cylinder and the Torus Tessellation and visibility representations of maps on the torus.Discrete & Computational Geometry, 19:249–263, 1998.doi:10.1007/PL00009344

Reference 38

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Observation 1d6a2368-a31b-4b6d-b8e5-555a275a0c13 · outbound

This paper cites Kobourov.

Rectangular Duals on the Cylinder and the Torus Kobourov

Reference 39

Resolution: unresolved; no resolver link, observed 2026-08-07T05:48:12.569252Z

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Observation 2be83981-60c7-4745-bbe3-bebada402207 · outbound

This paper cites Graph theoretic representation of architectural arrangement.Architectural Research and Teaching, pages 161–172, 1973.

Rectangular Duals on the Cylinder and the Torus Graph theoretic representation of architectural arrangement.Architectural Research and Teaching, pages 161–172, 1973

Reference 40

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:48:13.498330Z

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Observation 38f22417-3ea5-4e46-8c28-c74d8de4ee03 · outbound

This paper cites Springer-Verlag, 1980.

Rectangular Duals on the Cylinder and the Torus Springer-Verlag, 1980

Reference 41

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:48:13.481555Z

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Observation f40b179a-13d7-4ca4-b255-f6bf26dae86a · outbound

This paper cites On triangle cover contact graphs.Computational Geometry: Theory and Applications, 69:31– 38, 2018.doi:10.1016/J.COMGEO.2017.11.001.

Rectangular Duals on the Cylinder and the Torus On triangle cover contact graphs.Computational Geometry: Theory and Applications, 69:31– 38, 2018.doi:10.1016/J.COMGEO.2017.11.001

Reference 42

Resolution: verified exact; doi, observed 2026-08-07T05:48:12.715330Z

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Observation 0b197b63-39bf-43f2-ad0f-09e0e02e8a25 · outbound

This paper cites Tamassia and I.

Rectangular Duals on the Cylinder and the Torus Tamassia and I

Reference 43

Resolution: verified exact; doi, observed 2026-08-07T05:48:12.699423Z

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Observation 8294a64f-0ce7-48b1-8a08-be1ea07c9e27 · outbound

This paper cites Depth-first search and linear graph algorithms.SIAM Journal on Computing, 1(2):146–160, 1972.doi:10.1137/0201010.

Rectangular Duals on the Cylinder and the Torus Depth-first search and linear graph algorithms.SIAM Journal on Computing, 1(2):146–160, 1972.doi:10.1137/0201010

Reference 44

Resolution: unresolved; no resolver link, observed 2026-08-07T05:48:12.590922Z

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Observation 7d3f97df-9516-46c5-8db0-002b20a8f77b · outbound

This paper cites Interval representations of planar graphs.Journal of Combinatorial Theory, Series B, 40(1):9–20, 1986.doi:10.1016/0095-8956(86)90061-4.

Rectangular Duals on the Cylinder and the Torus Interval representations of planar graphs.Journal of Combinatorial Theory, Series B, 40(1):9–20, 1986.doi:10.1016/0095-8956(86)90061-4

Reference 45

Resolution: verified exact; doi, observed 2026-08-07T05:48:12.673412Z

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Observation 0585fa8c-95f9-45ef-9b8c-da97c72e5cfd · outbound

This paper cites On diagrams representing maps.Journal of the London Mathematical Society, 28(3):336–342, 1953.doi:10.1112/jlms/s1-28.3.336.

Rectangular Duals on the Cylinder and the Torus On diagrams representing maps.Journal of the London Mathematical Society, 28(3):336–342, 1953.doi:10.1112/jlms/s1-28.3.336

Reference 46

Resolution: verified exact; doi, observed 2026-08-07T05:48:12.658520Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation b695fd2f-69ba-4c3b-bb51-7f8ee9d5726c · outbound

This paper cites an unresolved cited work.

Rectangular Duals on the Cylinder and the Torus Unresolved cited work

Reference 47

Resolution: verified exact; doi, observed 2026-08-07T05:48:12.642436Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Pith citing papers

No inbound Pith citation observations are available.