XFF)-fr°unded families of graphs

Abstract

For any graph G, the First-Fit (or Grundy) chromatic number of G} denoted by XFF(G), k defined as the maximum number of colors used by the First-Fit (greedy) coloring of the vertices of G. We call a family JF of graphs ([removed] f(δ(G))t where δ(G) is the minimum degree of G. We first give some results concerning (δ, xFF)-bounded families and obtain a few such families. Then we prove that for any positive integer i) Forb(Kt9t) is ([removed] δ (G) + 1. We prove the validity of this conjecture for chordal graphs, complement of bipartite graphs and graphs with low minimum degree. © 2018 Utilitas Mathematica Publishing Incorporated. All rights reserved.