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arXiv · 1810.07825

Finding Maximal Sets of Laminar 3-Separators in Planar Graphs in Linear Time

David Eppstein·Bruce Reed
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Abstract

We consider decomposing a 3-connected planar graph $G$ using laminar separators of size three. We show how to find a maximal set of laminar 3-separators in such a graph in linear time. We also discuss how to find maximal laminar set of 3-separators from special families. For example we discuss non-trivial cuts, ie. cuts which split $G$ into two components of size at least two. For any vertex $v$, we also show how to find a maximal set of 3-separators disjoint from $v$ which are laminar and satisfy: every vertex in a separator $X$ has two neighbours not in the unique component of $G-X$ containing $v$. In all cases, we show how to construct a corresponding tree decomposition of adhesion three. Our new algorithms form an important component of recent methods for finding disjoint paths in nonplanar graphs.

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David Eppstein, Bruce Reed. 2018-10-17. Finding Maximal Sets of Laminar 3-Separators in Planar Graphs in Linear Time. https://arxiv.org/abs/1810.07825

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