The Krausz dimension of a graph

Abstract

A Krausz partition of a graph G is a partition of the edges of G into complete graphs, and the Krausz dimension of G is the minimum value of k for which there is a Krausz partition of G with no vertex in more than k of the complete graphs of the partition. We give some general results and bounds on the Krausz dimension and then study its behavior under various graph operations. A study is made of its value for the complete graph with one edge removed.