@article{47dd86798e5a4636982ee21d99202676,
title = "Monochromatic connected matchings in 2-edge-colored multipartite graphs",
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 {\L}uczak, 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.",
keywords = "Ramsey theory, connected matchings, paths",
author = "J{\'o}zsef Balogh and Alexandr Kostochka and Mikhail Lavrov and Xujun Liu",
note = "Funding Information: We thank Louis DeBiasio for helpful discussions. We also thank both referees for their detailed and helpful comments. Moreover, one of the referees suggested a nicer and shorter proof of Theorem 4 . Research of J{\'o}zsef Balogh is partially supported by NSF Grants DMS‐1500121 and DMS‐1764123, Arnold O. Beckman Research Award (UIUC) Campus Research Board 18132, and the Langan Scholar Fund (UIUC). Research of Alexandr Kostochka is supported in part by NSF grant DMS‐1600592, by UIUC Campus Research Board Award RB20003, and by grant 19‐01‐00682 of the Russian Foundation for Basic Research. The work was done while M. Lavrov was a postdoc at Department of Mathematics, University of Illinois at Urbana–Champaign. The work was partially done while X. Liu was a Ph.D. student at Department of Mathematics, University of Illinois at Urbana–Champaign. Research of this author was supported in part by Award RB17164 of the UIUC Campus Research Board. Publisher Copyright: {\textcopyright} 2022 Wiley Periodicals LLC.",
year = "2022",
month = jul,
doi = "10.1002/jgt.22797",
language = "English",
volume = "100",
pages = "578--607",
journal = "Journal of Graph Theory",
issn = "0364-9024",
number = "3",
}