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Hardness result for the total rainbow k-connection of graphs

Author

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  • Li, Wenjing
  • Li, Xueliang
  • Wu, Di

Abstract

A total-coloring of a graph G is a coloring of both the edge set E(G) and the vertex set V(G) of G. A path in a total-colored graph is called total-rainbow if its edges and internal vertices have distinct colors. For a positive integer k, a total-colored graph is called total-rainbow k-connected if for every two vertices of G there are k internally disjoint total-rainbow paths in G connecting them. For an ℓ-connected graph G and an integer k with 1 ≤ k ≤ ℓ, the total-rainbow k-connection number of G, denoted by trck(G), is the minimum number of colors needed in a total-coloring of G to make G total-rainbow k-connected. In this paper, we study the computational complexity of total-rainbow k-connection number of graphs. We show that it is NP-complete to decide whether trck(G)=3 for any fixed positive integer k.

Suggested Citation

  • Li, Wenjing & Li, Xueliang & Wu, Di, 2017. "Hardness result for the total rainbow k-connection of graphs," Applied Mathematics and Computation, Elsevier, vol. 305(C), pages 27-31.
    • Handle: RePEc:eee:apmaco:v:305:y:2017:i:c:p:27-31
    DOI: 10.1016/j.amc.2017.01.068
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