A different short proof of Brooks' theorem
Landon Rabern
TL;DR
This paper presents a novel, concise proof of Brooks' theorem by reducing to the cubic case and extends the result to online list coloring using the Kernel Lemma.
Contribution
It introduces a new short proof of Brooks' theorem through reduction to the cubic case and extends it to online list coloring.
Findings
New short proof of Brooks' theorem
Extension to online list coloring via Kernel Lemma
Reduction to the cubic case simplifies the proof
Abstract
Lov\'asz gave a short proof of Brooks' theorem by coloring greedily in a good order. We give a different short proof by reducing to the cubic case. Then we show how to extend the result to (online) list coloring via the Kernel Lemma.
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Taxonomy
TopicsAdvanced Graph Theory Research · Limits and Structures in Graph Theory · Graph Labeling and Dimension Problems