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Erdős–Gallai-type results for colorful monochromatic connectivity of a graph

Author

Listed:
  • Qingqiong Cai

    (Nankai University)

  • Xueliang Li

    (Nankai University)

  • Di Wu

    (Nankai University)

Abstract

A path in an edge-colored graph is called a monochromatic path if all the edges on the path are colored with one same color. An edge-coloring of G is a monochromatic connection coloring (MC-coloring, for short) if there is a monochromatic path joining any two vertices in G. For a connected graph G, the monochromatic connection number of G, denoted by mc(G), is defined to be the maximum number of colors used in an MC-coloring of G. These concepts were introduced by Caro and Yuster, and they got some nice results. In this paper, we study two kinds of Erdős–Gallai-type problems for mc(G), and completely solve them.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jcomop:v:33:y:2017:i:1:d:10.1007_s10878-015-9938-y
    DOI: 10.1007/s10878-015-9938-y
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    Citations

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    Cited by:

    1. 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.
    2. Jin, Zemin & Gui, Xueyao & Wang, Kaijun, 2021. "Multicolorful connectivity of trees," Applied Mathematics and Computation, Elsevier, vol. 402(C).
    3. 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.

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