The classification of f-coloring of graphs with large maximum degree

Abstract

Let G=(V,E) be a simple graph with vertex set V and edge set E. Define an integer-valued function f on V such that f(v) > 0 for every v ∈ V. An f-coloring of G is an edge-coloring of it such that each color class appears at every vertex v ∈ V(G) at most f(v) times. In this paper, we give a sufficient condition for a simple graph with large maximum degree to be of f-class 1.