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Monochromatic disconnection: Erdős-Gallai-type problems and product graphs

Author

Listed:
  • Ping Li

    (Center for Combinatorics and LPMC, Nankai University)

  • Xueliang Li

    (Center for Combinatorics and LPMC, Nankai University)

Abstract

For an edge-colored graph G, we call an edge-cut M of G monochromatic if the edges of M are colored with a same color. The graph G is called monochromatically disconnected if any two distinct vertices of G are separated by a monochromatic edge-cut. The monochromatic disconnection number, denoted by md(G), of a connected graph G is the maximum number of colors that are allowed to make G monochromatically disconnected. In this paper, we solve the Erdős-Gallai-type problems for the monochromatic disconnection, and give the monochromatic disconnection numbers for four graph products, i.e., Cartesian, strong, lexicographic, and tensor products.

Suggested Citation

  • Ping Li & Xueliang Li, 2022. "Monochromatic disconnection: Erdős-Gallai-type problems and product graphs," Journal of Combinatorial Optimization, Springer, vol. 44(1), pages 136-153, August.
    • Handle: RePEc:spr:jcomop:v:44:y:2022:i:1:d:10.1007_s10878-021-00820-3
    DOI: 10.1007/s10878-021-00820-3
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    References listed on IDEAS

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    1. Qingqiong Cai & Xueliang Li & Di Wu, 2017. "Erdős–Gallai-type results for colorful monochromatic connectivity of a graph," Journal of Combinatorial Optimization, Springer, vol. 33(1), pages 123-131, January.
    2. Qingqiong Cai & Xueliang Li & Di Wu, 2018. "Some extremal results on the colorful monochromatic vertex-connectivity of a graph," Journal of Combinatorial Optimization, Springer, vol. 35(4), pages 1300-1311, May.
    Full references (including those not matched with items on IDEAS)

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