Atlantic Graph Theory Seminar: James Preen (Cape Breton University)

There are many results about triangles in graphs, but the property that every edge in a graph is in at least one triangle seems not to have been studied before. The 4-regular case was quickly solved collaboratively following an internet posting and then written about by one author in their blog, before being published in the Journal of Graph Theory in 2013.

However, the result that was originally wanted was a characterisation for 5-regular graphs, and that did not emerge as smoothly. With no solution published several years later, I started working on it and have submiited my paper resolving it in 2021. In this talk I will outline the background and the ideas used in the proof, which involves cliques, multiple edges and a generalisation of the the line graph construction.

Join Zoom Meeting: link

To view previous slides and talks, click here.