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arXiv · 1601.01523

Partitioning a triangle-free planar graph into a forest and a forest of bounded degree

François Dross·Mickael Montassier·Alexandre Pinlou
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Abstract

An $({\cal F},{\cal F}_d)$-partition of a graph is a vertex-partition into two sets $F$ and $F_d$ such that the graph induced by $F$ is a forest and the one induced by $F_d$ is a forest with maximum degree at most $d$. We prove that every triangle-free planar graph admits an $({\cal F},{\cal F}_5)$-partition. Moreover we show that if for some integer $d$ there exists a triangle-free planar graph that does not admit an $({\cal F},{\cal F}_d)$-partition, then it is an NP-complete problem to decide whether a triangle-free planar graph admits such a partition.

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François Dross, Mickael Montassier, Alexandre Pinlou. 2016-01-07. Partitioning a triangle-free planar graph into a forest and a forest of bounded degree. https://arxiv.org/abs/1601.01523

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