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A Cauchy-Davenport type result for arbitrary regular graphs

Peter Hegarty (Institutionen för matematiska vetenskaper, matematik)
Integers (1867-0660). Vol. 11 (2011), 2, p. 227-235.
[Artikel, refereegranskad vetenskaplig]

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.

Nyckelord: Regular graph, graph powers, Cauchy-Davenport theorem

Denna post skapades 2012-06-19.
CPL Pubid: 159180


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