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On the asymptotic behavior of the independence number of a random (n, n)-tree

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Abstract

An (r, s)-tree is a connected, acyclic, bipartite graph withr light ands dark vertices. Uniform probability is assigned to the space,Γ(r, s), of (r, s)-trees. In this paper, we apply the probabilistic method to determine bounds for the vertex and the edge independence numbers for almost all (n, n)-trees inΓ(n,n). Consequently, we find that for almost all (n, n)-trees the percentage of dark vertices in a maximum matching is at least 72%.

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Authors and Affiliations

  1. Department of Mathematics, Michigan State University, 48824, E. Lansing, MI, USA

    J. H. Cho & E. M. Palmer

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  1. J. H. Cho
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  2. E. M. Palmer
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First author supported in part by grants from TGRC-KOSEF and BSRI 1409.

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Cho, J.H., Palmer, E.M. On the asymptotic behavior of the independence number of a random (n, n)-tree. Graphs and Combinatorics 12, 1–8 (1996). https://doi.org/10.1007/BF01858439

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