Degree tolerant coloring of graph

Abstract This paper initiates a study on a new coloring regime which sets conditions in respect of the degrees deg(v) and deg(u) where, v, u ∈ V(G) and vu ∈ E(G). This new coloring regime is called, ”degree tolerant coloring”. The degree tolerant chromatic number is defined. A number of interesting introductory results are presented. Amongst others, new Nordhaus-Gaddum type bounds are provided.