Regular Partitions of Regular Graphs

Abstract

In the study of the combinatorial structure of edge-graphs of convex polytopes one may ask whether a given graph possesses a partition consisting of certain kinds of subgraphs. In this paper we describe some special partitions of 3-valent and 4-valent graphs. These partitions can serve as examples for a type of partially ordered structures, called polystromas, which have recently been considered by Griinbaum [3].