All Questions

Let $n\geq m\geq0$ be two integers. The below binomial identity is provable by other means: $$\sum_{j=0}^m(-1)^j\binom{n+1}j2^{m-j} =\sum_{j=0}^m(-1)^j\binom{n-m+j}j.$$ QUESTION. Can you provide a ...

It is a well-known and cute exercise in algebraic graph theory to show that $K_{10}$ cannot be written as the edge-disjoint union of three copies of the Petersen graph $P$. Indeed, the graph $G$ whose ...

I need to give a math talk to a group of undergraduates. I am asking for advice because this talk will take place at a department picnic and there will be no blackboard or projector. I would like to ...

I'm teaching an introductory graph theory course in the Fall, which I'm excited about because it gives me the chance to improve my understanding of graphs (my work is in topology). A highlight for me ...