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arXiv · 1503.06822

Tree spanners of bounded degree graphs

Ioannis Papoutsakis
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Abstract

A tree $t$-spanner of a graph $G$ is a spanning tree of $G$ such that the distance between pairs of vertices in the tree is at most $t$ times their distance in $G$. Deciding tree $t$-spanner admissible graphs has been proved to be tractable for $t<3$ and NP-complete for $t>3$, while the complexity status of this problem is unresolved when $t=3$. For every $t>2$ and $b>0$, an efficient dynamic programming algorithm to decide tree $t$-spanner admissibility of graphs with vertex degrees less than $b$ is presented. Only for $t=3$, the algorithm remains efficient, when graphs $G$ with degrees less than $b\log |V(G)|$ are examined.

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Ioannis Papoutsakis. 2015-03-23. Tree spanners of bounded degree graphs. https://doi.org/10.1016/j.dam.2017.10.025

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