Rainbow matchings in Dirac bipartite graphs

Authors :: Universitat Politècnica de Catalunya. Doctorat en Matemàtica Aplicada
Universitat Politècnica de Catalunya. Departament de Matemàtiques
Universitat Politècnica de Catalunya. GAPCOMB - Geometric, Algebraic and Probabilistic Combinatorics
Coulson, Matthew John
Perarnau Llobet, Guillem
Universitat Politècnica de Catalunya. Doctorat en Matemàtica Aplicada
Universitat Politècnica de Catalunya. Departament de Matemàtiques
Universitat Politècnica de Catalunya. GAPCOMB - Geometric, Algebraic and Probabilistic Combinatorics
Coulson, Matthew John
Perarnau Llobet, Guillem
Publication Year :: 2019
Abstract: This is the peer reviewed version of the following article: Coulson, M, Perarnau, G. Rainbow matchings in Dirac bipartite graphs. Random Struct Alg. 2019; 55: 271– 289., which has been published in final form at https://doi.org/10.1002/rsa.20835. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions<br />We show the existence of rainbow perfect matchings in µn-bounded edge colorings of Dirac bipartite graphs, for a sufficiently small µ¿>¿0. As an application of our results, we obtain several results on the existence of rainbow k-factors in Dirac graphs and rainbow spanning subgraphs of bounded maximum degree on graphs with large minimum degree.<br />Postprint (author's final draft)

Tools