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
Choosability and edge choosability of planar graphs without five cycles
β Scribed by Weifan Wang; Ko-Wei Lih
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 402 KB
- Volume
- 15
- Category
- Article
- ISSN
- 0893-9659
No coin nor oath required. For personal study only.
β¦ Synopsis
It
is proved that a planar graph G without five cycles is three degenerate, hence, four choosable, and it is also edge-(A( G) + l)-h
π SIMILAR VOLUMES
## 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(_
The conjecture on acyclic 5-choosability of planar graphs [Borodin et al., 2002] as yet has been verified only for several restricted classes of graphs. None of these classes allows 4-cycles. We prove that a planar graph is acyclically 5-choosable if it does not contain an i-cycle adjacent to a j-cy
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## 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_
An L-list coloring of a graph G is a proper vertex coloring in which every vertex v receives a color from a prescribed list L(v). G is called k-choosable if all lists L(v) have the cardinality k and G is L-list colorable for all possible assignments of such lists. Recently, Thomassen has proved tha