Maximum induced matchings of random cubic graphs

Abstract

In this paper we present a heuristic for nding 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 dierential 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 satises 0: 2704n ≤|M|≤ 0: 2821n.