Fine structure of 4-critical triangle-free graphs III. General surfaces

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2018-01-01
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Dvorak, Zdenek
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Lidicky, Bernard
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Mathematics
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Dvořák, Král', and Thomas [Three-Coloring Triangle-Free Graphs on Surfaces IV. Bounding Face Sizes of 4-Critical Graphs, preprint, arXiv:1404.6356v3, 2015; Three-Coloring Triangle-Free Graphs on Surfaces VI. 3-Colorability of Quadrangulations, preprint, arXiv:1509.01013, 2015] gave a description of the structure of triangle-free graphs on surfaces with respect to 3-coloring. Their description, however, contains two substructures (both related to graphs embedded in a plane with two precolored cycles) whose coloring properties are not entirely determined. In this paper, we fill these gaps.

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This article is published as Dvorák, Zdenek, and Bernard Lidický. "Fine structure of 4-critical triangle-free graphs III. General surfaces." SIAM Journal on Discrete Mathematics 32, no. 1 (2018): 94-105. doi: 10.1137/15M1023403. Posted with permission.

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Mon Jan 01 00:00:00 UTC 2018
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