𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Choosability and edge choosability of planar graphs without five cycles

✍ 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.

✦ 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


πŸ“œ SIMILAR VOLUMES


Choosability, Edge Choosability, and Tot
✍ Wang Weifan; Ko-Wei Lih πŸ“‚ Article πŸ“… 2001 πŸ› Elsevier Science 🌐 English βš– 101 KB

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

Acyclic 5-choosability of planar graphs
✍ MickaΓ«l Montassier; AndrΓ© Raspaud; Weifan Wang πŸ“‚ Article πŸ“… 2007 πŸ› John Wiley and Sons 🌐 English βš– 188 KB πŸ‘ 1 views

## 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__‐list colorable if for a given list assignment __L__ = {__L__(__v__): __v__:β€‰βˆˆβ€‰__V__}, there exists a proper acyclic coloring ϕ of __G__ such that Ο•(_

Acyclic 5-choosability of planar graphs
✍ O. V. Borodin; A. O. Ivanova πŸ“‚ Article πŸ“… 2010 πŸ› John Wiley and Sons 🌐 English βš– 93 KB πŸ‘ 1 views

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

Choosability of toroidal graphs without
✍ Leizhen Cai; Weifan Wang; Xuding Zhu πŸ“‚ Article πŸ“… 2009 πŸ› John Wiley and Sons 🌐 English βš– 142 KB πŸ‘ 1 views

## Abstract Let __G__ be a toroidal graph without cycles of a fixed length __k__, and Ο‡~__l__~(__G__) the list chromatic number of __G__. We establish tight upper bounds of Ο‡~__l__~(__G__) for the following values of __k__: Β© 2009 Wiley Periodicals, Inc. J Graph Theory 65: 1–15, 2010.

Planar graphs without 4-cycles are acycl
✍ Weifan Wang; Min Chen πŸ“‚ Article πŸ“… 2009 πŸ› John Wiley and Sons 🌐 English βš– 190 KB

## 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__‐list colorable if for a given list assignment __L__={__L__(__v__)|__v__∈__V__}, there exists a proper acyclic coloring Ο€ of __G__ such that Ο€(__v__)∈_

A not 3-choosable planar graph without 3
✍ Margit Voigt πŸ“‚ Article πŸ“… 1995 πŸ› Elsevier Science 🌐 English βš– 140 KB

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