Maximum Induced Matchings of Random Cubic Graphs

Authors:
William Duckworth;Nicholas C. Wormald;Michele Zito
Affiliations:
-;-;-
Venue:
COCOON '00 Proceedings of the 6th Annual International Conference on Computing and Combinatorics
Year:
2000

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Abstract

In this paper we present a heuristic for finding a large induced matching M 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 returned by the algorithm. The corresponding upper bound is derived by means of a direct expectation argument. We prove that M asymptotically almost surely satisfies 0.2704n ≤ |M| ≤ 0.2821n.