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arXiv · 2204.09113

Representation of short distances in structurally sparse graphs

Zdeněk Dvořák
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Abstract

A partial orientation $\vec{H}$ of a graph $G$ is a weak $r$-guidance system if for any two vertices at distance at most $r$ in $G$, there exists a shortest path $P$ between them such that $\vec{H}$ directs all but one edge in $P$ towards this edge. In case $\vec{H}$ has bounded maximum outdegree, this gives an efficient representation of shortest paths of length at most $r$ in $G$. We show that graphs from many natural graph classes admit such weak guidance systems, and study the algorithmic aspects of this notion.

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Zdeněk Dvořák. 2022-04-19. Representation of short distances in structurally sparse graphs. https://arxiv.org/abs/2204.09113

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