On Graphs that do not Contain a Thomsen Graph

Abstract

A Thomsen graph [2, p. 22] consists of six vertices partitioned into two classes of three each, with every vertex in one class connected to every vertex in the other; it is the graph of the “gas, water, and electricity” problem [1, p. 206]. (All graphs considered in this paper will be undirected, having neither loops nor multiple edges.)