Trees maximizing the number of almost-perfect matchings

作     者：Cambie, Stijn McCoy, Bradley Sharma, Gunjan Wagner, Stephan Yap, Corrine 

作者机构：Department of Computer Science KU Leuven Campus Kulak-Kortrijk Kortrijk Belgium Department of Computer Science James Madison University HarrisonburgVA United States Applied Mathematics Illinois Institute of Technology ChicagoIL United States Institute of Discrete Mathematics TU Graz Graz Austria Department of Mathematics Uppsala University Uppsala Sweden School of Mathematics Georgia Institute of Technology AtlantaGA United States 

出 版 物：《arXiv》 (arXiv)

年 卷 期：2022年

核心收录：

主　　题：Forestry 

摘      要：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 *** Codes 05C05 05C09 05C35 05C05 05C09 05C35 05C05, 05C09, 05C35, 05C70 © 2022, CC BY.