• Citer

Squared Chromatic Number Without Claws or Large Cliques

par Cames Van Batenburg, Wouter ;KANG, ROSS J.
Référence Canadian mathematical bulletin, 62, 1, page (23-35)
Publication Publié, 2019-03-01

Article révisé par les pairs

• Accès en ligne
• Détails
• Contenu
• Statistiques

Résumé :

Let G be a claw-free graph on n vertices with clique number ω, and consider the chromatic number χ(G 2 ) of the square G 2 of G. Writing χ′ s (d) for the supremum of χ(L 2 ) over the line graphs L of simple graphs of maximum degree at most d, we prove that χ(G 2 ) ≤ χ′ s (ω) for ω ∈ {3, 4}. For ω = 3, this implies the sharp bound χ(G 2 ) ≤ 10. For ω = 4, this implies χ(G 2 ) ≤ 22, which is within 2 of the conjectured best bound. This work is motivated by a strengthened form of a conjecture of Erdos and Nešetřil.