Large k-separated matchings of random regular graphs

Authors:
Mihalis Beis;William Duckworth;Michele Zito
Affiliations:
University of Liverpool, Liverpool, UK;Macquarie University, Sydney, NSW, Australia;University of Liverpool, Liverpool, UK
Venue:
ACSC '05 Proceedings of the Twenty-eighth Australasian conference on Computer Science - Volume 38
Year:
2005

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Abstract

A k-separated matching in a graph is a set of edges at distance at least k from one another (hence, for instance, a 1-separated matching is just a matching in the classical sense). We consider the problem of approximating the solution to the maximum k-separated matching problem in random r-regular graphs for each fixed integer k and each fixed r ≥ 3. We prove both constructive lower bounds and combinatorial upper bounds on the size of the optimal solutions.