Linear choosability of graphs
A proper vertex coloring of a non oriented graph $G=(V,E)$ is linear if the graph induced by the vertices of two color classes is a forest of paths. A graph $G$ is $L$-list colorable if for a given list assignment $L=\{L(v): v∈V\}$, there exists a proper coloring $c$ of $G$ such that $c(v)∈L(v)$ for...
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| Format: | Article |
| Language: | English |
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Discrete Mathematics & Theoretical Computer Science
2005-01-01
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| Series: | Discrete Mathematics & Theoretical Computer Science |
| Subjects: | |
| Online Access: | https://dmtcs.episciences.org/3434/pdf |
| _version_ | 1797270366769381376 |
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| author | Louis Esperet Mickael Montassier André Raspaud |
| author_facet | Louis Esperet Mickael Montassier André Raspaud |
| author_sort | Louis Esperet |
| collection | DOAJ |
| description | A proper vertex coloring of a non oriented graph $G=(V,E)$ is linear if the graph induced by the vertices of two color classes is a forest of paths. A graph $G$ is $L$-list colorable if for a given list assignment $L=\{L(v): v∈V\}$, there exists a proper coloring $c$ of $G$ such that $c(v)∈L(v)$ for all $v∈V$. If $G$ is $L$-list colorable for every list assignment with $|L(v)|≥k$ for all $v∈V$, then $G$ is said $k$-choosable. A graph is said to be lineary $k$-choosable if the coloring obtained is linear. In this paper, we investigate the linear choosability of graphs for some families of graphs: graphs with small maximum degree, with given maximum average degree, planar graphs... Moreover, we prove that determining whether a bipartite subcubic planar graph is lineary 3-colorable is an NP-complete problem. |
| first_indexed | 2024-04-25T02:03:08Z |
| format | Article |
| id | doaj.art-9db66e890e4144c29890d336e12b7934 |
| institution | Directory Open Access Journal |
| issn | 1365-8050 |
| language | English |
| last_indexed | 2024-04-25T02:03:08Z |
| publishDate | 2005-01-01 |
| publisher | Discrete Mathematics & Theoretical Computer Science |
| record_format | Article |
| series | Discrete Mathematics & Theoretical Computer Science |
| spelling | doaj.art-9db66e890e4144c29890d336e12b79342024-03-07T14:41:15ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1365-80502005-01-01DMTCS Proceedings vol. AE,...Proceedings10.46298/dmtcs.34343434Linear choosability of graphsLouis Esperet0https://orcid.org/0000-0001-6200-0514Mickael Montassier1André Raspaud2Laboratoire Bordelais de Recherche en InformatiqueLaboratoire Bordelais de Recherche en InformatiqueLaboratoire Bordelais de Recherche en InformatiqueA proper vertex coloring of a non oriented graph $G=(V,E)$ is linear if the graph induced by the vertices of two color classes is a forest of paths. A graph $G$ is $L$-list colorable if for a given list assignment $L=\{L(v): v∈V\}$, there exists a proper coloring $c$ of $G$ such that $c(v)∈L(v)$ for all $v∈V$. If $G$ is $L$-list colorable for every list assignment with $|L(v)|≥k$ for all $v∈V$, then $G$ is said $k$-choosable. A graph is said to be lineary $k$-choosable if the coloring obtained is linear. In this paper, we investigate the linear choosability of graphs for some families of graphs: graphs with small maximum degree, with given maximum average degree, planar graphs... Moreover, we prove that determining whether a bipartite subcubic planar graph is lineary 3-colorable is an NP-complete problem.https://dmtcs.episciences.org/3434/pdfvertex-coloringlistacyclic3-frugalchoosability under constraints.[info.info-dm] computer science [cs]/discrete mathematics [cs.dm][math.math-co] mathematics [math]/combinatorics [math.co] |
| spellingShingle | Louis Esperet Mickael Montassier André Raspaud Linear choosability of graphs Discrete Mathematics & Theoretical Computer Science vertex-coloring list acyclic 3-frugal choosability under constraints. [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] [math.math-co] mathematics [math]/combinatorics [math.co] |
| title | Linear choosability of graphs |
| title_full | Linear choosability of graphs |
| title_fullStr | Linear choosability of graphs |
| title_full_unstemmed | Linear choosability of graphs |
| title_short | Linear choosability of graphs |
| title_sort | linear choosability of graphs |
| topic | vertex-coloring list acyclic 3-frugal choosability under constraints. [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] [math.math-co] mathematics [math]/combinatorics [math.co] |
| url | https://dmtcs.episciences.org/3434/pdf |
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