Zdeněk Dvořák, Daniel Kráľ, Robin Thomas
Published 2014-02-19, updated 2019-04-16Version 2
We show that the size of a 4-critical graph of girth at least five is bounded by a linear function of its genus. This strengthens the previous bound on the size of such graphs given by Thomassen. It also serves as the basic case for the description of the structure of 4-critical triangle-free graphs embedded in a fixed surface, presented in a future paper of this series.
Comments: 53 pages, 7 figures; updated according to referee remarks
4-critical graphs on surfaces without contractible (<=4)-cycles
Three-coloring triangle-free graphs on surfaces II. 4-critical graphs in a disk
Three-coloring triangle-free graphs on surfaces IV. Bounding face sizes of 4-critical graphs
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