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.
- Uppsala University Sweden
- Georgia Institute of Technology United States
- Illinois Institute of Technology United States
- Mississippi School for Mathematics and Science United States
- American Mathematical Society United States
maximal matching, matching, 05C05 05C09 05C35 05C05 05C09 05C35 05C05, 05C09, 05C35, 05C70, trees, Trees, Graphical indices (Wiener index, Zagreb index, Randić index, etc.), Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.), almost-perfect matching, FOS: Mathematics, Mathematics - Combinatorics, weighted Hosoya index, Combinatorics (math.CO)
maximal matching, matching, 05C05 05C09 05C35 05C05 05C09 05C35 05C05, 05C09, 05C35, 05C70, trees, Trees, Graphical indices (Wiener index, Zagreb index, Randić index, etc.), Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.), almost-perfect matching, FOS: Mathematics, Mathematics - Combinatorics, weighted Hosoya index, Combinatorics (math.CO)
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