Trees maximizing the number of almost-perfect matchings
Copyright policy )Trees maximizing the number of almost-perfect matchings
We characterize the extremal trees that maximize the number of almost- perfect matchings, which are matchings covering all but one or two vertices, and those that maximize the number of strong almost-perfect matchings, which are matchings missing only one or two leaves. We also determine the trees that minimize the number of maximal matchings. We apply these results to extremal problems on the weighted Hosoya index for several choices of vertex-degree-based weight function.
- Georgia Institute of Technology United States
- James Madison University United States
- Mississippi School for Mathematics and Science United States
- KU Leuven Belgium
- American Mathematical Society United States
maximal matching, 0199 Other Mathematical Sciences, Mathematics, Applied, 05C05 05C09 05C35 05C05 05C09 05C35 05C05, 05C09, 05C35, 05C70, 0101 Pure Mathematics, Trees, Weighted Hosoya index, Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.), almost-perfect matching, FOS: Mathematics, Matching, Mathematics - Combinatorics, weighted Hosoya index, INDEX, Science & Technology, 0103 Numerical and Computational Mathematics, matching, Maximal matching, trees, Graphical indices (Wiener index, Zagreb index, Randić index, etc.), Physical Sciences, 4904 Pure mathematics, Almost-perfect matching, Combinatorics (math.CO), Mathematics
maximal matching, 0199 Other Mathematical Sciences, Mathematics, Applied, 05C05 05C09 05C35 05C05 05C09 05C35 05C05, 05C09, 05C35, 05C70, 0101 Pure Mathematics, Trees, Weighted Hosoya index, Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.), almost-perfect matching, FOS: Mathematics, Matching, Mathematics - Combinatorics, weighted Hosoya index, INDEX, Science & Technology, 0103 Numerical and Computational Mathematics, matching, Maximal matching, trees, Graphical indices (Wiener index, Zagreb index, Randić index, etc.), Physical Sciences, 4904 Pure mathematics, Almost-perfect matching, Combinatorics (math.CO), Mathematics
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