A graph G = G(EE) with lists L(v), associated with its vertices v E V, is called L-list colourable if there is a proper vertex colouring of G in which the colour assigned to a vertex v is chosen from L(v). We say G is k-choosable if there is at least one L-list colouring for every possible list assi
The complexity of planar graph choosability
β Scribed by Shai Gutner
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 553 KB
- Volume
- 159
- Category
- Article
- ISSN
- 0012-365X
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π SIMILAR VOLUMES
We prove the statement of the title, which was conjectured in 1975 by V. G. Vizing and, independently, in 1979 by P. ErdΓΆs, A. L. Rubin, and H. Taylor. (i) 1994 Academic Press, Inc.
An L-list coloring of a graph G is a proper vertex coloring in which every vertex v gets a color from a list L(v) of allowed colors. G is called k-choosable if all lists L(v) have exactly k elements and if G is L-list colorable for all possible assignments of such lists. Verifying conjectures of Erd
## Abstract A proper vertex coloring of a graph __G__β=β(__V,E__) is acyclic if __G__ contains no bicolored cycle. A graph __G__ is acyclically __L__βlist colorable if for a given list assignment __L__β=β{__L__(__v__): __v__:βββ__V__}, there exists a proper acyclic coloringβΟβof __G__ such that Ο(_
Let Ο l (G), Ο l (G), Ο l (G), and (G) denote, respectively, the list chromatic number, the list chromatic index, the list total chromatic number, and the maximum degree of a non-trivial connected outerplane graph G. We prove the following results. ( 1 and only if G is an odd cycle. This proves the
## Abstract A proper vertex coloring of a graph __G__=(__V, E__) is acyclic if __G__ contains no bicolored cycle. A graph __G__ is acyclically __L__βlist colorable if for a given list assignment __L__={__L__(__v__)|__v__β__V__}, there exists a proper acyclic coloring Ο of __G__ such that Ο(__v__)β_