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On total rainbow k-connected graphs

Author

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  • Sun, Yuefang
  • Jin, Zemin
  • Li, Fengwei

Abstract

A total-colored graph G is total rainbow connected if any two vertices are connected by a path whose edges and inner vertices have distinct colors. A graph G is total rainbow k-connected if there is a total-coloring of G with k colors such that G is total rainbow connected. The total rainbow connection number, denoted by trc(G), of a graph G is the smallest k to make G total rainbow k-connected. For n, k ≥ 1, define h(n, k) to be the minimum size of a total rainbow k-connected graph G of order n. In this paper, we prove a sharp upper bound for trc(G) in terms of the number of vertex-disjoint cycles of G. We also compute exact values and upper bounds for h(n, k).

Suggested Citation

  • Sun, Yuefang & Jin, Zemin & Li, Fengwei, 2017. "On total rainbow k-connected graphs," Applied Mathematics and Computation, Elsevier, vol. 311(C), pages 223-227.
    • Handle: RePEc:eee:apmaco:v:311:y:2017:i:c:p:223-227
    DOI: 10.1016/j.amc.2017.05.020
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