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A Cauchy–Davenport Type Result for Arbitrary Regular Graphs

Peter Hegarty
  • Mathematical Sciences, Chalmers University of Technology and University of Gothenburg, SE-41296 Gothenburg, Sweden.
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Published Online: 2011-04-11 | DOI: https://doi.org/10.1515/integ.2011.019

Abstract

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.

Keywords.: Regular graph; graph powers; Cauchy–Davenport theorem

About the article

Received: 2010-09-30

Accepted: 2011-01-01

Published Online: 2011-04-11

Published in Print: 2011-04-01


Citation Information: Integers, Volume 11, Issue 2, Pages 227–235, ISSN (Print) 1867-0652, DOI: https://doi.org/10.1515/integ.2011.019.

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