Interval non-total colorable graphs (Միջակայքային տոտալ ներկում չունեցող գրաֆներ)

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.