Mathematical Citation Quotient (MCQ) 2018: 0.40
A Cauchy–Davenport Type Result for Arbitrary Regular Graphs
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 ∈ > 0 such that, if 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 + ∈ times the number of edges in . We discuss a range of further questions to which this result gives rise.
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