What is the difference between a square and a triangle?

Abstract

We offer a reader-friendly introduction to the attracting edge problem (also known as the "triangle conjecture") and its most general current solution of Limic and Tarrès (2007). Little original research is reported; rather this article ``zooms in'' to describe the essential characteristics of two different techniques/approaches verifying the almost sure existence of the attracting edge for the strongly edge reinforced random walk (SERRW) on a square. Both arguments extend straightforwardly to the SERRW on even cycles. Finally, we show that the case where the underlying graph is a triangle cannot be studied by a simple modification of either of the two techniques.

18 pages, 1 figure