List-k-Coloring H-Free Graphs for All k>4

Given an integer k > 4 and a graph H , we prove that, assuming P ≠ NP, the List- k -Coloring Problem restricted to H -free graphs can be solved in polynomial time if and only if either every component of H is a path on at most three vertices, or removing the isolated vertices of H leaves an induc...

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Bibliographic Details
Published in:Combinatorica (Budapest. 1981) Vol. 44; no. 5; pp. 1063 - 1068
Main Authors: Chudnovsky, Maria, Hajebi, Sepehr, Spirkl, Sophie
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.10.2024
Springer Nature B.V
Subjects:
Apexes
Coloring
Combinatorics
Graph theory
Graphs
Mathematics
Mathematics and Statistics
Original Paper
Polynomials
Coloring
Polynomial-time Algorithms
List-Coloring
Induced subgraphs
ISSN:0209-9683, 1439-6912
Online Access:Get full text
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Summary:Given an integer k > 4 and a graph H , we prove that, assuming P ≠ NP, the List- k -Coloring Problem restricted to H -free graphs can be solved in polynomial time if and only if either every component of H is a path on at most three vertices, or removing the isolated vertices of H leaves an induced subgraph of the five-vertex path. In fact, the “if” implication holds for all k ≥ 1 .
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ISSN:0209-9683
1439-6912
DOI:10.1007/s00493-024-00106-2