List Colouring Trees in Logarithmic Space

June 20, 2022 · The Ethereal · 🏛 Embedded Systems and Applications

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Authors Hans L. Bodlaender, Carla Groenland, Hugo Jacob arXiv ID 2206.09750 Category cs.DM: Discrete Mathematics Cross-listed cs.CC, cs.DS Citations 8 Venue Embedded Systems and Applications Last Checked 2 months ago
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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