Maximum induced matchings of random cubic graphs

Authors:
W. Duckworth;N. C. Wormald;M. Zito
Affiliations:
Department of Mathematics & Statistics, University of Melbourne, Vic, Australia;Department of Mathematics & Statistics, University of Melbourne, Vic, Australia;Department of Computer Science, University of Liverpool, UK
Venue:
Journal of Computational and Applied Mathematics - Special issue: Probabilistic methods in combinatorics and combinatorial optimization
Year:
2002

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Abstract

We present a heuristic for finding a large induced matching of cubic graphs. We analyse the performance of this heuristic, which is a random greedy algorithm, on random cubic graphs using differential equations and obtain a lower bound on the expected size of the induced matching, M, returned by the algorithm. A corresponding upper bound is derived by means of a direct expectation argument. We prove that M asymptotically almost surely satisfies 0.270413n ≤|M| ≤ 0.282069n.