2
votes
2answers
369 views

Decomposition of $K_{10}$ in copies of the Petersen graph

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 ...
12
votes
11answers
2k views

Giving a math talk with no blackboard or projector

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 ...
15
votes
4answers
2k views

The Matrix-Tree Theorem without the matrix

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 ...