Monochromatic connected matchings in 2‐edge‐colored multipartite graphs

@article{Balogh2019MonochromaticCM,
  title={Monochromatic connected matchings in 2‐edge‐colored multipartite graphs},
  author={J{\'o}zsef Balogh and Alexandr V. Kostochka and Mikhail Lavrov and Xujun Liu},
  journal={Journal of Graph Theory},
  year={2019},
  volume={100},
  pages={578 - 607}
}
A matching M $M$ in a graph G $G$ is connected if all the edges of M $M$ are in the same component of G $G$ . 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… 
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