Debski, M and Lonc, Z and Rzazewski, Pavel Michael (2017) Sequences of radius k for complete bipartite graphs. DISCRETE APPLIED MATHEMATICS, 225. pp. 51-63. ISSN 0166-218X 10.1016/j.dam.2017.03.017

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Abstract

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. (C) 2017 Elsevier B.V. All rights reserved.

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