Paper Citation Record · LEDGER

Transductions of Graph Classes Admitting Product Structure

As of 19 August 2026, this Paper Citation Record lists 19 of 19 outbound references and 3 inbound Pith citation observations for arXiv:2501.18326.

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

pith.paper-citation-record.v1
2501.18326 v4

Coverage vector

measured 19 of 19 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-10T00:03:59.865779Z

measured 22 of 22 standing notices

One-hop event checks from named stored sources.

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

measured 3 of 3 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-09T14:12:32.881181Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-24T03:33:50.849782Z

Reference resolution

19 of 19 outbound references displayed

verified exact1
verified fuzzy1
unresolved13
parse uncertain0
malformed identifier3
metadata mismatch1

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 72b06aac-5ebd-4203-8eae-8bc3f26635fb · outbound

This paper cites On the complexity of embedding in graph products.

Transductions of Graph Classes Admitting Product Structure On the complexity of embedding in graph products

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T00:04:30.333741Z

Source-reported events for the cited work

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

Observation 26c5d952-c0c5-4ca1-8144-2f7a723f18c3 · outbound

This paper cites 10 Jan Dreier.

Transductions of Graph Classes Admitting Product Structure 10 Jan Dreier

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-10T00:03:59.821608Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b92df22e-cd37-4c31-90f5-13eb57833eb3 · outbound

This paper cites 14 Vida Dujmovic, Pat Morin, and David R.

Transductions of Graph Classes Admitting Product Structure 14 Vida Dujmovic, Pat Morin, and David R

Reference 8

Resolution: malformed identifier; doi_truncated, observed 2026-08-10T00:04:00.047384Z

Source-reported events for the cited work

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

Observation 58a83a71-752c-4ccc-90c6-d568d9ce3b00 · outbound

This paper cites 3D-grids are not transducible from planar graphs.

Transductions of Graph Classes Admitting Product Structure 3D-grids are not transducible from planar graphs

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-10T00:03:59.842191Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ed6e9ff2-1882-4180-8de4-f966fa744e72 · outbound

This paper cites 1137/22m1540296,doi:10.1137/22M1540296.

Transductions of Graph Classes Admitting Product Structure 1137/22m1540296,doi:10.1137/22M1540296

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-10T00:03:59.849290Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1355cb78-8244-4946-988f-87317f8cce2a · outbound

This paper cites Hereditary Graph Product Structure and $\cal H$-clique-width.

Transductions of Graph Classes Admitting Product Structure Hereditary Graph Product Structure and $\cal H$-clique-width

Reference 15

Resolution: metadata mismatch; local_arxiv, observed 2026-08-10T00:04:15.266696Z

Source-reported events for the cited work

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

Observation 94c63193-4827-4587-9bfd-3c0c05e31b3b · outbound

This paper cites CSL.2022.31,doi:10.4230/LIPICS.CSL.2022.31.

Transductions of Graph Classes Admitting Product Structure CSL.2022.31,doi:10.4230/LIPICS.CSL.2022.31

Reference 16

Resolution: malformed identifier; no resolver link, observed 2026-08-10T00:03:59.856085Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4f0d7025-5b84-4cae-8125-d451bf1e67a8 · outbound

This paper cites 26 Michał Pilipczuk.

Transductions of Graph Classes Admitting Product Structure 26 Michał Pilipczuk

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-10T00:03:59.859383Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation feb19cae-c161-4e10-9c8a-b026a294a829 · outbound

This paper cites Graph classes through the lens of logic.

Transductions of Graph Classes Admitting Product Structure Graph classes through the lens of logic

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-10T00:03:59.862588Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a3576879-5167-4dec-9c48-e577f74738cb · outbound

This paper cites 28 Szymon Toruńczyk.

Transductions of Graph Classes Admitting Product Structure 28 Szymon Toruńczyk

Reference 1971

Resolution: unresolved; no resolver link, observed 2026-08-10T00:03:59.865779Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 450d6a7d-c570-4477-a8ea-2368550584b8 · outbound

This paper cites 8 Bruno Courcelle, Johann A.

Transductions of Graph Classes Admitting Product Structure 8 Bruno Courcelle, Johann A

Reference 1990

Resolution: verified exact; doi, observed 2026-08-10T00:04:00.070093Z

Source-reported events for the cited work

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

Observation f3668993-147d-4a22-a065-f248a6b4a474 · outbound

This paper cites 9 Marc Distel, Robert Hickingbotham, Tony Huynh, and David R.

Transductions of Graph Classes Admitting Product Structure 9 Marc Distel, Robert Hickingbotham, Tony Huynh, and David R

Reference 2000

Resolution: unresolved; no resolver link, observed 2026-08-10T00:03:59.818233Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b91df524-14d3-45b1-981a-48076f158982 · outbound

This paper cites 20 Martin Grohe, Stephan Kreutzer, Roman Rabinovich, Sebastian Siebertz, and Konstantinos S.

Transductions of Graph Classes Admitting Product Structure 20 Martin Grohe, Stephan Kreutzer, Roman Rabinovich, Sebastian Siebertz, and Konstantinos S

Reference 2019

Resolution: unresolved; no resolver link, observed 2026-08-10T00:03:59.845943Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d4269c32-c276-480e-afd8-66ec9ede2646 · outbound

This paper cites 13 Vida Dujmovic, Gwenaël Joret, Piotr Micek, Pat Morin, and David R.

Transductions of Graph Classes Admitting Product Structure 13 Vida Dujmovic, Gwenaël Joret, Piotr Micek, Pat Morin, and David R

Reference 2020

Resolution: unresolved; no resolver link, observed 2026-08-10T00:03:59.824661Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5e4cddc7-ac52-4f5b-81c3-b6a1f278c1b0 · outbound

This paper cites First-order transducibility among classes of sparse graphs.

Transductions of Graph Classes Admitting Product Structure First-order transducibility among classes of sparse graphs

Reference 2021

Resolution: unresolved; no resolver link, observed 2026-08-10T00:03:59.834331Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 592ca249-1113-4487-991d-677c0ad8d2d8 · outbound

This paper cites On first-order transductions of classes of graphs.

Transductions of Graph Classes Admitting Product Structure On first-order transductions of classes of graphs

Reference 2022

Resolution: unresolved; no resolver link, observed 2026-08-10T00:03:59.810917Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ce5d789f-3f45-461f-b981-8a8b82c056d6 · outbound

This paper cites 2023.03.004,doi:10.1016/J.JCTB.2023.03.004.

Transductions of Graph Classes Admitting Product Structure 2023.03.004,doi:10.1016/J.JCTB.2023.03.004

Reference 2023

Resolution: malformed identifier; no resolver link, observed 2026-08-10T00:03:59.830659Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 58004c93-589b-4589-b89c-3bcd0b5608a1 · outbound

This paper cites On first-order transductions of classes of graphs.

Transductions of Graph Classes Admitting Product Structure On first-order transductions of classes of graphs

Reference 2024

Resolution: unresolved; no resolver link, observed 2026-08-10T00:03:59.807086Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation af6b5718-7b9e-4ea2-9965-af7eabc7c23d · outbound

This paper cites First-order transducibility among classes of sparse graphs.

Transductions of Graph Classes Admitting Product Structure First-order transducibility among classes of sparse graphs

Reference 2025

Resolution: unresolved; no resolver link, observed 2026-08-10T00:03:59.838309Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

Observation 5a4bb216-a641-4b46-8aec-18ba15ab7c55 · inbound

Hereditary Graph Product Structure and $\cal H$-clique-width cites this paper.

Hereditary Graph Product Structure and $\cal H$-clique-width Transductions of Graph Classes Admitting Product Structure

Reference 17

Resolution: verified exact; arxiv_id, observed 2026-05-24T03:33:50.852232Z

Source-reported events for the cited work

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

Observation 13f05797-34c6-44e2-8c6c-8321dae86f37 · inbound

Short Paths in the Planar Graph Product Structure Theorem cites this paper.

Short Paths in the Planar Graph Product Structure Theorem Transductions of Graph Classes Admitting Product Structure

Reference 41

Resolution: unresolved; no resolver link, observed 2026-08-09T14:12:32.881181Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3d768e71-7b3c-42cc-b4fc-727c1952a4c0 · inbound

First-order transducibility among classes of sparse graphs cites this paper.

First-order transducibility among classes of sparse graphs Transductions of Graph Classes Admitting Product Structure

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-07T15:22:47.919103Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.