Maximum Induced Matchings of Random Cubic Graphs

  • William Duckworth
  • Nicholas C. Wormald
  • Michele Zito
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1858)


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.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • William Duckworth
    • 1
  • Nicholas C. Wormald
    • 1
  • Michele Zito
    • 2
  1. 1.Department of Mathematics and StatisticsUniversity of MelbourneAustralia
  2. 2.Department of Computer ScienceUniversity of LiverpoolUK

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