Date: 21 Jul 2000

Maximum Induced Matchings of Random Cubic Graphs

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In this paper we present a heuristic for finding a large induced matching \( \mathcal{M} \) 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 \( \mathcal{M} \) asymptotically almost surely satisfies 0:2704n < | \( \mathcal{M} \) | < 0:2821n.

Supported by the Australian Research Council
Supported by EPSRC grant GR/L/77089