Coloring graphs with no even hole \(\geqslant 6\): the triangle-free case
The electronic journal of combinatorics, Tome 24 (2017) no. 3
In this paper, we prove that the class of graphs with no triangle and no induced cycle of even length at least 6 has bounded chromatic number. It is well-known that even-hole-free graphs are $\chi$-bounded but we allow here the existence of $C_4$. The proof relies on the concept of Parity Changing Path, an adaptation of Trinity Changing Path which was recently introduced by Bonamy, Charbit and Thomassé to prove that graphs with no induced cycle of length divisible by three have bounded chromatic number.
DOI :
10.37236/5351
Classification :
05C15, 05C38
Mots-clés : graph coloring, forbidding cycles, even hole, trinity changing path
Mots-clés : graph coloring, forbidding cycles, even hole, trinity changing path
Affiliations des auteurs :
Aurélie Lagoutte 1
@article{10_37236_5351,
author = {Aur\'elie Lagoutte},
title = {Coloring graphs with no even hole \(\geqslant 6\): the triangle-free case},
journal = {The electronic journal of combinatorics},
year = {2017},
volume = {24},
number = {3},
doi = {10.37236/5351},
zbl = {1367.05076},
url = {http://geodesic.mathdoc.fr/articles/10.37236/5351/}
}
Aurélie Lagoutte. Coloring graphs with no even hole \(\geqslant 6\): the triangle-free case. The electronic journal of combinatorics, Tome 24 (2017) no. 3. doi: 10.37236/5351
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