A pair of mathematicians solved a legendary question about the proportion of vertices in a graph with an odd number of connections. “It’s a bit of a surprise, at least for me, that such a combination ...

Forbes contributors publish independent expert analyses and insights. I help people communicate data clearly with graphs. Graphs are pictorial representations of numbers. Therefore, at the least, we ...

If true, the following conjecture of Thomassen [Th81] is a planarity criterion for a special class of graphs that involves only K 5. Recall that a planar graph on n vertices contains at most 3n-6 ...

A cooperator is someone who pays a cost, c, for another individual to receive a benefit, b. A defector pays no cost and does not distribute any benefits. In evolutionary biology, cost and benefit are ...

This is a preview. Log in through your library . Abstract Let HG(x, y) be the expected hitting time from vertex x to vertex y for the first time on a simple connected graph G and φ(G) = ...