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
Graphs of degree 4 are 5-edge-choosable
β Scribed by Juvan, Martin; Mohar, Bojan; ??krekovski, Riste
- Publisher
- John Wiley and Sons
- Year
- 1999
- Tongue
- English
- Weight
- 312 KB
- Volume
- 32
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
β¦ Synopsis
It is shown that every simple graph with maximal degree 4 is 5-edgechoosable.
π SIMILAR VOLUMES
## 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_
## Abstract Improper choosability of planar graphs has been widely studied. In particular, Ε krekovski investigated the smallest integer __g__~k~ such that every planar graph of girth at least __g__~k~ is __k__βimproper 2βchoosable. He proved [9] that 6ββ€β__g__~1~ β€β9; 5ββ€β __g__~2~ββ€β7; 5ββ€β__g__~3
## Abstract An __acyclic__ edge coloring of a graph is a proper edge coloring such that there are no bichromatic cycles. The __acyclic chromatic index__ of a graph is the minimum number __k__ such that there is an acyclic edge coloring using __k__ colors and is denoted by __a__β²(__G__). It was conj
## Abstract A graph __H__ is light in a given class of graphs if there is a constant __w__ such that every graph of the class which has a subgraph isomorphic to __H__ also has a subgraph isomorphic to __H__ whose sum of degrees in __G__ is β€β__w__. Let $\cal G$ be the class of simple planar graphs
## Abstract It is proved that, if __s__ β₯ 2, a graph that does not have __K__~2~β+β__K__~__s__~β=β__K__~1~β+β__K__~1, __s__~ as a minor is (__s__,β1)\*βchoosable. This completes the proof that such a graph is (__s__β+β1βββ__d__,__d__)\*βchoosable whenever 0ββ€β__d__ββ€β__s__ββ1 Β© 2003 Wiley Periodica