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Three-coloring triangle-free graphs on surfaces III. Graphs of girth five
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.Comment: 53 pages, 7 figures; updated according to referee remark
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