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Combinatorica

, Volume 1, Issue 4, pp 369–376 | Cite as

Matching behaviour is asymptotically normal

  • C. D. Godsil
Article

Abstract

Ak-matching in a graphG is a set ofk edges, no two of which have a vertex in common. The number of these inG is writtenp(G, k). Using an idea due to L. H. Harper, we establish a condition under which these numbers are approximately normally distributed. We show that our condition is satisfied ifn=|V(G)| is large compared to the maximum degree Δ of a vertex inG(i.e. Δ=o(n)) orG is a large complete graph. One corollary of these results is that the number of points fixed by a randomly chosen involution in the symmetric groupS is asymptotically normally distributed.

AMS subject classification (1980)

05 A 15 05 C 50 60 F 05 

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Copyright information

© Akadémiai Kiadó 1981

Authors and Affiliations

  • C. D. Godsil
    • 1
    • 2
  1. 1.Institut für Mathematik Montanuniversität LeobenLeobenAustria
  2. 2.Simon Fraser UniversityBurnabyCanada

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