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arXiv · 1711.05091

Sequences of radius $k$ for complete bipartite graphs

Michał Dębski·Zbigniew Lonc·Paweł Rzążewski
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Abstract

A \emph{$k$-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 $k>1$.

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Michał Dębski, Zbigniew Lonc, Paweł Rzążewski. 2017-11-14. Sequences of radius $k$ for complete bipartite graphs. https://doi.org/10.1016/j.dam.2017.03.017

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