Department of Applied Mathematics, University of Twente
Abstract
We introduce and study backbone colorings, a variation on classical vertex colorings: Given a graph G=(V,E) and a spanning subgraph H of G (the backbone of G), a backbone coloring for G and H is a proper vertex coloring V→{1,2,…} of G in which the colors assigned to adjacent vertices in H differ by at least two. We study the cases where the backbone is either a spanning tree or a spanning path