Monochromatic connected matchings in 2-edge-colored multipartite graphs

József Balogh, Alexandr Kostochka, Mikhail Lavrov, Xujun Liu

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)578-607
Number of pages30
JournalJournal of Graph Theory
Issue number3
StatePublished - Jul 2022


  • Ramsey theory
  • connected matchings
  • paths

ASJC Scopus subject areas

  • Geometry and Topology
  • Discrete Mathematics and Combinatorics


Dive into the research topics of 'Monochromatic connected matchings in 2-edge-colored multipartite graphs'. Together they form a unique fingerprint.

Cite this