List packing number of bounded degree graphs

List packing number of bounded degree graphs

We investigate the list packing number of a graph, the least \(k\) such that there are always \(k\) disjoint proper list-colourings whenever we have lists all of size \(k\) associated to the vertices. We are curious how the behaviour of the list packing number contrasts with that of the list chromat...

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Veröffentlicht in:arXiv.org 2023-03
Hauptverfasser: Cambie, Stijn, Wouter Cames van Batenburg, Davies, Ewan, Kang, Ross J
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Mathematics - Combinatorics
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Wouter Cames van Batenburg
Davies, Ewan
Kang, Ross J
description We investigate the list packing number of a graph, the least \(k\) such that there are always \(k\) disjoint proper list-colourings whenever we have lists all of size \(k\) associated to the vertices. We are curious how the behaviour of the list packing number contrasts with that of the list chromatic number, particularly in the context of bounded degree graphs. The main question we pursue is whether every graph with maximum degree \(\Delta\) has list packing number at most \(\Delta+1\). Our results highlight the subtleties of list packing and the barriers to, for example, pursuing a Brooks'-type theorem for the list packing number.
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title List packing number of bounded degree graphs
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