Trees maximizing the number of almost-perfect matchings

Autor:	Cambie, Stijn, McCoy, Bradley, Sharma, Gunjan, Wagner, Stephan, Yap, Corrine
Rok vydání:	2022
Předmět:	Mathematics - Combinatorics 05C05 05C09 05C35 05C05 05C09 05C35 05C05 05C09 05C35 05C70
Druh dokumentu:	Working Paper
Popis:	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. Comment: 21 pages, 8 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2209.03408 Zobrazit plný text záznamu View this record from Arxiv