A Cauchy-Davenport type result for arbitrary regular graphs
Journal article, 2011
Motivated by the Cauchy-Davenport theorem for sumsets, and its interpretation in terms of Cayley graphs, we prove the following main result: There is a universal constant e > 0 such that, if G is a connected, regular graph on n vertices, then either every pair of vertices can be connected by a path of length at most three, or the number of pairs of such
vertices is at least 1+e times the number of edges in G.
We discuss a range of further questions to which this result gives rise.