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- W2616177764 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)." @default.
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- W2616177764 date "2017-10-01" @default.
- W2616177764 modified "2023-09-25" @default.
- W2616177764 title "On total rainbow k -connected graphs" @default.
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- W2616177764 doi "https://doi.org/10.1016/j.amc.2017.05.020" @default.
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