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 ...

Abstract: The b-chromatic number of a graph, written as φ(G), is the highest number of colors you can use to color the graph properly, with one special rule: in each color group, there must be at ...

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) = ...

The Annals of Applied Probability, Vol. 16, No. 1 (Feb., 2006), pp. 295-309 (15 pages) We consider the discrete Laplace operator $\Delta ^{(N)}$ on Erdős-Rényi random graphs with N vertices and edge ...