Odd-K4K4’s in stability critical graphs

A subdivision of K4K4 is called an odd-K4K4 if each triangle of the K4K4 is subdivided to form an odd cycle, and is called a fully odd-K4K4 if each of the six edges of the K4K4 is subdivided into a path of odd length. A graph GG is called stability critical if the deletion of any edge from GG increases the stability number. In 1993, Sewell and Trotter conjectured that in a stability critical graph every triple of edges which share a common end is contained in a fully odd-K4K4. The purpose of this note is to show that such a triple is contained in an odd-K4K4.