Coloring graphs with no even hole ≥ 6: the triangle-free case

Aurélie Lagoutte (1)

1 G-SCOP_OC - Optimisation Combinatoire

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 χ-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.

Mots clés: graph coloring; forbidding cycles; Trinity Changing Path

Domaines: Mathématique discrète [cs.DM]; Combinatoire [math.CO]

Aurélie Lagoutte. Coloring graphs with no even hole ≥ 6: the triangle-free case. The Electronic Journal of Combinatorics, 2017, 24 (3), pp.#P3.8. ⟨10.37236/5351⟩. ⟨hal-01566608⟩