Finding small-width connected path decompositions in polynomial time

Dariusz Dereniowski; Dorota Osula; Paweł Rzążewski

doi:10.1016/j.tcs.2019.03.039

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arXiv · 1802.05501

Finding small-width connected path decompositions in polynomial time

Dariusz Dereniowski·Dorota Osula·Paweł Rzążewski

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Abstract

A connected path decomposition of a simple graph $G$ is a path decomposition $(X_1,\ldots,X_l)$ such that the subgraph of $G$ induced by $X_1\cup\cdots\cup X_i$ is connected for each $i\in\{1,\ldots,l\}$. The connected pathwidth of $G$ is then the minimum width over all connected path decompositions of $G$. We prove that for each fixed $k$, the connected pathwidth of any input graph can be computed in polynomial-time. This answers an open question raised by Fedor V. Fomin during the GRASTA 2017 workshop, since connected pathwidth is equivalent to the connected (monotone) node search game.

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BibTeX RIS

Dariusz Dereniowski, Dorota Osula, Paweł Rzążewski. 2018-02-15. Finding small-width connected path decompositions in polynomial time. https://doi.org/10.1016/j.tcs.2019.03.039

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