Chapter

Computing and Combinatorics

Volume 1858 of the series Lecture Notes in Computer Science pp 34-43

Date:

Maximum Induced Matchings of Random Cubic Graphs

  • William DuckworthAffiliated withDepartment of Mathematics and Statistics, University of Melbourne
  • , Nicholas C. WormaldAffiliated withDepartment of Mathematics and Statistics, University of Melbourne
  • , Michele ZitoAffiliated withDepartment of Computer Science, University of Liverpool

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Abstract

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.