Abstract

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.

Keywords

  1. coloring
  2. planar graphs
  3. surfaces

MSC codes

  1. 05C15
  2. 05C75

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References

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Information & Authors

Information

Published In

cover image SIAM Journal on Discrete Mathematics
SIAM Journal on Discrete Mathematics
Pages: 94 - 105
ISSN (online): 1095-7146

History

Submitted: 28 May 2015
Accepted: 24 July 2017
Published online: 9 January 2018

Keywords

  1. coloring
  2. planar graphs
  3. surfaces

MSC codes

  1. 05C15
  2. 05C75

Authors

Affiliations

Funding Information

Czech Science Foundation : 14-19503S
National Science Foundation https://doi.org/10.13039/100000001 : DMS-1266016, DMS-1600390

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