Abstract

A total coloring of a graph G is a coloring of its vertices and edges such that no adjacent vertices, edges, and no incident vertices and edges obtain the same color. An interval total t-coloring of a graph G is a total coloring of G with colors 1,2,…,t such that all colors are used, and the edges incident to each vertex v together with v are colored by dG(v)+1 consecutive colors, where dG(v) is the degree of a vertex v in G. In this paper we describe some methods for constructing of graphs that have no interval total coloring.

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