Matchings in starlike trees |
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| Affiliation: | Faculty of Science, University of Kragujevac P. O. Box 60, YU-34000 Kragujevac, Yugoslavia;Departamento de Matemática, Facultad de Ciencias Universidad de Los Andes, Mérida 5101, Venezuela |
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| Abstract: | Let m(G,k) be the number of k-matchings in the graph G. We write G1 ⪯ G2 if m(G1, k) ≤ m(G2, k) for all k = 1, 2,…. A tree is said to be starlike if it possesses exactly one vertex of degree greater than two. The relation T1 ⪯ T2 is shown to hold for various pairs of starlike trees T1, T2. The starlike trees (with a given number of vertices), extremal with respect to the relation ⪯, are characterized. |
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