A note on circular chromatic number of graphs with large girth and similar problems

Jaroslav Nesetril (1) , Patrice Ossona de Mendez (1, 2)

1 IUUK - Computer Science Institute of Charles University [Prague]
2 CAMS - Centre d'Analyse et de Mathématique sociales

In this short note, we extend the result of Galluccio, Goddyn, and Hell, which states that graphs of large girth excluding a minor are nearly bipartite. We also prove a similar result for the oriented chromatic number, from which follows in particular that graphs of large girth excluding a minor have oriented chromatic number at most $5$, and for the $p$th chromatic number $\chi_p$, from which follows in particular that graphs $G$ of large girth excluding a minor have $\chi_p(G)\leq p+2$.

Domaines: Combinatoire [math.CO]

Jaroslav Nesetril, Patrice Ossona de Mendez. A note on circular chromatic number of graphs with large girth and similar problems. 2014. ⟨hal-00946134⟩