[r, s, t]-colourings of paths

Abstract

Tyt. z nagł.References p. 149.Dostępny również w formie drukowanej.ABSTRACT: The concept of colourings was recently introduced by Hackmann, Kemnitz and Marangio as follows: Given non-negative integers r, s and t, an [r, s, t]-colouring of a graph is a mapping c to the colour set such that for every two adjacent vertices vi, vj, for every two adjacent edges ei, ej, for all pairs of incident vertices and edges, respectively. The [r, s, t]-chromatic number is defined to be the minimum k such that G admits an [r, s, t]-colouring. In this paper, we determine the [r, s, t]-chromatic number for paths. KEYWORDS: Total colouring, paths