Trees maximizing the number of almost-perfect matchings
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866915165011705856 |
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| author | Cambie, Stijn McCoy, Bradley Sharma, Gunjan Wagner, Stephan Yap, Corrine |
| author_facet | Cambie, Stijn McCoy, Bradley Sharma, Gunjan Wagner, Stephan Yap, Corrine |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_03408 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Trees maximizing the number of almost-perfect matchings Cambie, Stijn McCoy, Bradley Sharma, Gunjan Wagner, Stephan Yap, Corrine Combinatorics 05C05 05C09 05C35 05C05 05C09 05C35 05C05, 05C09, 05C35, 05C70 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. |
| title | Trees maximizing the number of almost-perfect matchings |
| topic | Combinatorics 05C05 05C09 05C35 05C05 05C09 05C35 05C05, 05C09, 05C35, 05C70 |
| url | https://arxiv.org/abs/2209.03408 |