Bipartite multigraphs with expander-like properties

Authors:
Lars Engebretsen
Affiliations:
Department of Numerical Analysis and Computer Science, Royal Institute of Technology, SE-100 44 Stockholm, Sweden
Venue:
Discrete Applied Mathematics
Year:
2007

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Abstract

This note considers the following combinatorial question: ''For which integers d and functions f"d does there exist, for every large enough v, a bipartite d-regular multigraph on 2v nodes with node sets V and W having the following property: For every U that is a subset of either V or W, the cardinality of the set of neighbours of U is at least f"d(|U|)?'' Graphs with the above property seem to behave well also with respect to other, more complicated, expander-like properties. We provide results for d in {5,6,7,8} and give a description of a fairly general methodology for devising computer-assisted proofs for a wide class of mathematical claims using interval arithmetic.