2018/10/11 by Jurgen Kritschgau, Kritschgau, J\''{u}rgen
Mathematics · Computer Science · #Limits and Structures in Graph Theory #Advanced Graph Theory Research
paper · pdf · doi:10.48550/arxiv.1810.05324
The existence of a rainbow matching given a minimum color degree, proper\ncoloring, or triangle-free host graph has been studied extensively. This paper,\ngeneralizes these problems to edge colored graphs with given total color\ndegree. In particular, we find that if a graph G has total color degree 2mn\nand satisfies some other properties, then G contains a matching of size m;\nThese other properties include G being triangle-free, C4-free, properly\ncolored, or large enough.\n