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arXiv · 1404.6356

Three-coloring triangle-free graphs on surfaces IV. Bounding face sizes of 4-critical graphs

Zdenek Dvorak·Daniel Kral·Robin Thomas
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Abstract

Let G be a 4-critical graph with t triangles, embedded in a surface of genus g. Let c be the number of 4-cycles in G that do not bound a 2-cell face. We prove that the sum of lengths of (>=5)-faces of G is at most linear in g+t+c-1.

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Zdenek Dvorak, Daniel Kral, Robin Thomas. 2020-08-04. Three-coloring triangle-free graphs on surfaces IV. Bounding face sizes of 4-critical graphs. https://arxiv.org/abs/1404.6356

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