bibkey: dvorak2020singleconflict authors: “Zdeněk Dvořák; Louis Esperet; Ross J. Kang; Kenta Ozeki” year: 2020 title: “Single-conflict colouring” doi: 10.48550/arXiv.1803.10962 url: https://arxiv.org/abs/1803.10962v2 claim: “A local edge assignment forbids one ordered pair of endpoint colours; multiple conflicts on one vertex pair are represented by parallel edges.” strata_touched: [] license: citation-only triage: anchor

Ordered colour conflicts

The inspected primary text is arXiv:1803.10962v2, deposited 9 October 2020. Section 1, printed page 2, defines a local colour assignment on each end of every multigraph edge. A permitted vertex colouring must avoid choosing both endpoint colours specified by any edge. A list of several forbidden ordered pairs is represented by parallel edges.

For prime-coordinate avoidance, a vertex represents a prime and a colour represents a permitted first residue. A selected forbidden residue pair is exactly such an edge conflict. Local alphabets can be relabelled; their unequal prime sizes and the higher prime-power prefixes require the separate arithmetic argument in the covering report. This note attests the conflict model, not that argument or a universal existence theorem for its arithmetic inputs.

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