2017 saw the centennial of William Tutte, one of the greatest mathematicians of modern times.  One of the testimonies to Tutte’s genius is that nearly everything he did proved to be a catalyst, triggering an explosion of further investigations and

I will discuss a few examples where considering loops leads to interesting insights, often allowing unifying existing results. These examples will include cops and robbers games, graph homomorphisms, variants of interval and chordal graphs, and versions of domination. Join Zoom

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