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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| Vydané v: | Combinatorica (Budapest. 1981) Ročník 44; číslo 5; s. 1063 - 1068 |
|---|---|
| Hlavní autori: | , , |
| Médium: | Journal Article |
| Jazyk: | English |
| Vydavateľské údaje: |
Berlin/Heidelberg
Springer Berlin Heidelberg
01.10.2024
Springer Nature B.V |
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| ISSN: | 0209-9683, 1439-6912 |
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| Abstract | 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
. |
|---|---|
| AbstractList | 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
. 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. |
| Author | Chudnovsky, Maria Spirkl, Sophie Hajebi, Sepehr |
| Author_xml | – sequence: 1 givenname: Maria surname: Chudnovsky fullname: Chudnovsky, Maria organization: Princeton University – sequence: 2 givenname: Sepehr surname: Hajebi fullname: Hajebi, Sepehr email: shajebi@uwaterloo.ca organization: Department of Combinatorics and Optimization, University of Waterloo – sequence: 3 givenname: Sophie surname: Spirkl fullname: Spirkl, Sophie organization: Department of Combinatorics and Optimization, University of Waterloo |
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| Cites_doi | 10.1002/jgt.22028 10.1137/0210055 10.1137/21M1443352 10.1016/0196-6774(83)90032-9 10.1016/0304-3975(86)90184-2 10.1137/0202019 10.1007/s00453-013-9777-0 10.7551/mitpress/12274.003.0038 |
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| Copyright | The Author(s), under exclusive licence to János Bolyai Mathematical Society and Springer-Verlag GmbH Germany, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
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| Keywords | Coloring Polynomial-time Algorithms List-Coloring Induced subgraphs |
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| References | Holyer (CR5) 1981; 10 Couturier, Golovach, Kratsch, Paulusma (CR1) 2015; 71 Hajebi, Li, Spirkl (CR4) 2022; 36 Golovach, Johnson, Paulusma, Song (CR3) 2017; 84 Kamiński, Lozin (CR7) 2007; 2 Hopcroft, Karp (CR6) 1973; 2 CR8 Leven, Galil (CR9) 1983; 4 Edwards (CR2) 1986; 43 PA Golovach (106_CR3) 2017; 84 J-F Couturier (106_CR1) 2015; 71 S Hajebi (106_CR4) 2022; 36 JE Hopcroft (106_CR6) 1973; 2 M Kamiński (106_CR7) 2007; 2 D Leven (106_CR9) 1983; 4 I Holyer (106_CR5) 1981; 10 106_CR8 K Edwards (106_CR2) 1986; 43 |
| References_xml | – volume: 84 start-page: 331 issue: 4 year: 2017 end-page: 363 ident: CR3 article-title: A survey on the computational complexity of coloring graphs with forbidden subgraphs publication-title: J. Graph Theory doi: 10.1002/jgt.22028 – volume: 10 start-page: 718 issue: 4 year: 1981 end-page: 720 ident: CR5 article-title: The NP-completeness of edge-coloring publication-title: SIAM J. Comput. doi: 10.1137/0210055 – volume: 36 start-page: 2004 issue: 3 year: 2022 end-page: 2027 ident: CR4 article-title: Complexity dichotomy for list-5-coloring with a forbidden induced subgraph publication-title: SIAM J. Discrete Math. doi: 10.1137/21M1443352 – volume: 4 start-page: 35 issue: 1 year: 1983 end-page: 44 ident: CR9 article-title: NP completeness of finding the chromatic index of regular graphs publication-title: J. Algorithms doi: 10.1016/0196-6774(83)90032-9 – volume: 43 start-page: 337 issue: 2–3 year: 1986 end-page: 343 ident: CR2 article-title: The complexity of colouring problems on dense graphs publication-title: Theoret. Comput. Sci. doi: 10.1016/0304-3975(86)90184-2 – ident: CR8 – volume: 2 start-page: 225 year: 1973 end-page: 231 ident: CR6 article-title: An algorithm for maximum matchings in bipartite graphs publication-title: SIAM J. Comput. doi: 10.1137/0202019 – volume: 2 start-page: 61 issue: 1 year: 2007 end-page: 66 ident: CR7 article-title: Coloring edges and vertices of graphs without short or long cycles publication-title: Contrib. Discrete Math. – volume: 71 start-page: 21 issue: 1 year: 2015 end-page: 35 ident: CR1 article-title: List coloring in the absence of a linear forest publication-title: Algorithmica doi: 10.1007/s00453-013-9777-0 – volume: 36 start-page: 2004 issue: 3 year: 2022 ident: 106_CR4 publication-title: SIAM J. Discrete Math. doi: 10.1137/21M1443352 – volume: 43 start-page: 337 issue: 2–3 year: 1986 ident: 106_CR2 publication-title: Theoret. Comput. Sci. doi: 10.1016/0304-3975(86)90184-2 – volume: 10 start-page: 718 issue: 4 year: 1981 ident: 106_CR5 publication-title: SIAM J. Comput. doi: 10.1137/0210055 – ident: 106_CR8 doi: 10.7551/mitpress/12274.003.0038 – volume: 84 start-page: 331 issue: 4 year: 2017 ident: 106_CR3 publication-title: J. Graph Theory doi: 10.1002/jgt.22028 – volume: 71 start-page: 21 issue: 1 year: 2015 ident: 106_CR1 publication-title: Algorithmica doi: 10.1007/s00453-013-9777-0 – volume: 2 start-page: 61 issue: 1 year: 2007 ident: 106_CR7 publication-title: Contrib. Discrete Math. – volume: 4 start-page: 35 issue: 1 year: 1983 ident: 106_CR9 publication-title: J. Algorithms doi: 10.1016/0196-6774(83)90032-9 – volume: 2 start-page: 225 year: 1973 ident: 106_CR6 publication-title: SIAM J. Comput. doi: 10.1137/0202019 |
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| Snippet | 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... 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... |
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| SubjectTerms | Apexes Coloring Combinatorics Graph theory Graphs Mathematics Mathematics and Statistics Original Paper Polynomials |
| Title | List-k-Coloring H-Free Graphs for All k>4 |
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