List packing of graphs with bounded tree-width
Masaki Kashima, Shun-ichi Maezawa, Xuding Zhu

TL;DR
This paper investigates list packing numbers of graphs with bounded tree-width, establishing bounds and exact values for specific cases, and shows that related decision problems are solvable efficiently.
Contribution
It improves bounds on the maximum packing number for graphs with bounded tree-width and proves linear-time solvability of related decision problems.
Findings
Proves that for d ≥ 3, t(d) ≤ 2d - 1.
Establishes that for d ≥ 2, t(d) ≥ d + 2.
Shows that determining if χ_l^{ extasteriskcentered}(G) ≤ k is solvable in linear time for fixed d, k.
Abstract
Assume is a -assignment of a graph . An -packing of is a sequence of -mappings such that each is an -coloring of , and for each vertex of , (and hence when ). We say is list -packable if for any -assignment of , there is an -packing of . The list packing number of is the minimum integer such that is -packable. For a positive integer , let be the maximum packing number of graphs of tree-width at most . It was known that for any . In this paper, we prove that for , and for . In particular, and . Furthermore, we show that for constant positive integers , the problem of…
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