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arXiv · 2206.09750

List Colouring Trees in Logarithmic Space

Hans L. Bodlaender·Carla Groenland·Hugo Jacob
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Abstract

We show that List Colouring can be solved on $n$-vertex trees by a deterministic Turing machine using $O(\log n)$ bits on the worktape. Given an $n$-vertex graph $G=(V,E)$ and a list $L(v)\subseteq\{1,\dots,n\}$ of available colours for each $v\in V$, a list colouring for $G$ is a proper colouring $c$ such that $c(v)\in L(v)$ for all $v$.

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Hans L. Bodlaender, Carla Groenland, Hugo Jacob. 2022-06-20. List Colouring Trees in Logarithmic Space. https://arxiv.org/abs/2206.09750

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