Families of Disjoint Sets Colouring Technique and Concept of Common and Non Common Vertex

Abstract

Families of disjoint sets colouring technique is trial to generalize all type of colouring, such as edge colouring, vertex colouring, face colouring, sets colouring (partition of sets into families of disjoint sets). In this paper we introduce the concept of common vertex between two cliques and more than two cliques. We introduce some results related to concept of common and non common vertex, and introduce some results explain the number of minimum colour classes not changed after addition or after removal of non common vertex, if maximum clique number is constant. Also in this paper we introduce concept of quasi non common vertex between two cliques and more than two cliques and we introduce some results related to this concept.