Matching behaviour is asymptotically normal |
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Authors: | C D Godsil |
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Institution: | 1. Institut für Mathematik Montanuniversit?t Leoben, A-8700, Leoben, Austria 2. Simon Fraser University, V5A 1S6, Burnaby, B. C., Canada
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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. |
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Keywords: | 05 A 15 05 C 50 60 F 05 |
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