Beautiful conjectures in graph theory

Beautiful conjectures in graph theory

Three conjectures in extremal spectral graph theory

We prove three conjectures regarding the maximization of spectral invariants over certain families of graphs. Our most difficult result is that the join of P2 and Pn−2 is the unique graph of maximum spectral radius over all planar graphs. This was conjectured by Boots and Royle in 1991 and independently by Cao and Vince in 1993. Similarly, we prove a conjecture of Cvetković and Rowlinson from 1...

Sketchy Tweets: Ten Minute Conjectures in Graph Theory

Following this advice, we should look over the big questions, then doodle and sketch out some approaches. If you are an expert, then this is easy to do, but most people do not want to wait to become an expert before looking at interesting problems. Graph theory, our area of expertise, has many hard-to-solve questions. Some hark back to the recreational roots of the area yet still keep their mys...

Domains and Two Conjectures in Dimension Theory

This note investigates two long-standing conjectures on the Krull dimension of integer-valued polynomial rings and of polynomial rings, respectively , in the context of (locally) essential domains.

Some conjectures looking for a NCG theory

It is pointed out that ambiguities in the regularization of actions with second derivatives seem to happen with the same multiplicity that the standard model of elementary particles