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A Criterion for Vertex Colorability of a Graph Stated in Terms of Edge Orientations

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arxiv 0712.1884 v1 pith:BSFSVJJL submitted 2007-12-12 math.CO

Yu. V. Matiyasevich This is my paper · ORCID
classification math.CO
keywords colorabilitycriteriacriteriongivengraphstatedtermsvertex
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L.M.Vitaver [1962] and G.I.Minty [1962] suggested criteria for vertex colorability of a graph in at most a given number of colors; these criteria are stated in terms of the orientation of the edges. One additional criterion of this kind is given here.

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  1. The Heawood approach to Tait colorings and defining vertex sets

    math.CO 2024-11 conditional novelty 5.0 of 10

    For non-bipartite planar cubic graphs with 2n vertices, the Heawood system has rank n+1, giving a defining set of n-1 vertices and at most 3 times 2^{n-1} Tait colorings; circular ladders have 2^n+8 colorings for even...

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