Monochromatic connected matchings in 2-edge-colored multipartite graphs
Department
Mathematics
Document Type
Article
Publication Date
7-1-2022
Abstract
A matching (Formula presented.) in a graph (Formula presented.) is connected if all the edges of (Formula presented.) are in the same component of (Formula presented.). Following Łuczak, there have been many results using the existence of large connected matchings in cluster graphs with respect to regular partitions of large graphs to show the existence of long paths and other structures in these graphs. We prove exact Ramsey-type bounds on the sizes of monochromatic connected matchings in 2-edge-colored multipartite graphs. In addition, we prove a stability theorem for such matchings.
Journal Title
Journal of Graph Theory
Journal ISSN
03649024
Volume
100
Issue
3
First Page
578
Last Page
607
Digital Object Identifier (DOI)
10.1002/jgt.22797
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