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List-k-Coloring H-Free Graphs for All $$k>4$$
Combinatorica ( IF 1.0 ) Pub Date : 2024-05-14 , DOI: 10.1007/s00493-024-00106-2 Maria Chudnovsky , Sepehr Hajebi , Sophie Spirkl
更新日期：2024-05-15
Combinatorica ( IF 1.0 ) Pub Date : 2024-05-14 , DOI: 10.1007/s00493-024-00106-2 Maria Chudnovsky , Sepehr Hajebi , Sophie Spirkl
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Given an integer \(k>4\) and a graph H, we prove that, assuming P\(\ne \) 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 \(k\ge 1\).
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