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.

graph powers

Regular graph

Cauchy-Davenport theorem

Chalmers, Mathematical Sciences, Mathematics

University of Gothenburg

1867-0660 (ISSN)

Vol. 11 2 227-235Basic sciences

Other Mathematics