✦ LIBER ✦

Choosability of toroidal graphs without short cycles

✍ Scribed by Leizhen Cai; Weifan Wang; Xuding Zhu

Publisher: John Wiley and Sons
Year: 2009
Tongue: English
Weight: 142 KB
Volume: 65
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.20460

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

Let G be a toroidal graph without cycles of a fixed length k, and χ~l~(G) the list chromatic number of G. We establish tight upper bounds of χ~l~(G) for the following values of k:
© 2009 Wiley Periodicals, Inc. J Graph Theory 65: 1–15, 2010.

📜 SIMILAR VOLUMES

Acyclic 5-choosability of planar graphs

Acyclic 5-choosability of planar graphs without adjacent short cycles

✍ O. V. Borodin; A. O. Ivanova 📂 Article 📅 2010 🏛 John Wiley and Sons 🌐 English ⚖ 93 KB 👁 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

Acyclic 5-choosability of planar graphs

Acyclic 5-choosability of planar graphs without small cycles

✍ Mickaël Montassier; André Raspaud; Weifan Wang 📂 Article 📅 2007 🏛 John Wiley and Sons 🌐 English ⚖ 188 KB 👁 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__: ∈ __V__}, there exists a proper acyclic coloring ϕ of __G__ such that ϕ(_

The 4-Choosability of Plane Graphs witho

The 4-Choosability of Plane Graphs without 4-Cycles

✍ Peter Che Bor Lam; Baogang Xu; Jiazhuang Liu 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 179 KB

A graph G is called k-choosable if k is a number such that if we give lists of k colors to each vertex of G there is a vertex coloring of G where each vertex receives a color from its own list no matter what the lists are. In this paper, it is shown that each plane graph without 4-cycles is 4-choosa

Planar graphs without 4-cycles are acycl

Planar graphs without 4-cycles are acyclically 6-choosable

✍ Weifan Wang; Min Chen 📂 Article 📅 2009 🏛 John Wiley and Sons 🌐 English ⚖ 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 π of __G__ such that π(__v__)∈_

Coloring Graphs without Short Non-boundi

Coloring Graphs without Short Non-bounding Cycles

✍ S. Fisk; B. Mohar 📂 Article 📅 1994 🏛 Elsevier Science 🌐 English ⚖ 357 KB

It is shown that there is a constant \(c\) such that if \(G\) is a graph embedded in a surface of genus \(g\) (either orientable or non-orientable) and the length of a shortest non-bounding cycle of \(G\) is at least \(c \log (g+1)\), then \(G\) is six-colorable. A similar result holds for three- an

Vertex colorings of graphs without short

Vertex colorings of graphs without short odd cycles

✍ Andrzej Dudek; Reshma Ramadurai 📂 Article 📅 2010 🏛 John Wiley and Sons 🌐 English ⚖ 118 KB 👁 1 views

Motivated by the work of Nešetřil and R ödl on "Partitions of vertices" we are interested in obtaining some quantitative extensions of their result. In particular, given a natural number r and a graph G of order m with odd girth g, we show the existence of a graph H with odd girth at least g and ord