Sequences of radius k for complete bipartite graphs

11/14/2017

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by   Michał Dębski, et al.

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A k-radius sequence for a graph G is a sequence of vertices of G (typically with repetitions) such that for every edge uv of G vertices u and v appear at least once within distance k in the sequence. The length of a shortest k-radius sequence for G is denoted by f_k(G). We give an asymptotically tight estimation on f_k(G) for complete bipartite graphs which matches a lower bound, valid for all bipartite graphs. We also show that determining f_k(G) for an arbitrary graph G is NP-hard for every constant k>1.