✦ LIBER ✦

Extending colorings of locally planar graphs

✍ Scribed by Michael O. Albertson; Joan P. Hutchinson

Publisher: John Wiley and Sons
Year: 2001
Tongue: English
Weight: 112 KB
Volume: 36
Category: Article
ISSN: 0364-9024
DOI: 10.1002/1097-0118(200102)36:2<105::aid-jgt5>3.0.co;2-h

No coin nor oath required. For personal study only.

✦ Synopsis

Suppose G is a graph embedded in S g with width (also known as edge width) at least 264(2 g À 1). If P V(G) is such that the distance between any two vertices in P is at least 16, then any 5-coloring of P extends to a 5-coloring of all of G. We present similar extension theorems for 6-and 7-chromatic toroidal graphs, for 3-colorable large-width graphs embedded on S g with every face even-sided, and for 4-colorable largewidth Eulerian triangulations.

📜 SIMILAR VOLUMES

Total colorings of planar graphs with la

Total colorings of planar graphs with large maximum degree

✍ Borodin, O. V.; Kostochka, A. V.; Woodall, D. R. 📂 Article 📅 1997 🏛 John Wiley and Sons 🌐 English ⚖ 97 KB 👁 2 views

It is proved that a planar graph with maximum degree ∆ ≥ 11 has total (vertex-edge) chromatic number ∆ + 1.

Acrylic improper colorings of graphs

✍ Boiron, P.; Sopena, E.; Vignal, L. 📂 Article 📅 1999 🏛 John Wiley and Sons 🌐 English ⚖ 153 KB 👁 2 views

In this article, we introduce the new notion of acyclic improper colorings of graphs. An improper coloring of a graph is a vertex-coloring in which adjacent vertices are allowed to have the same color, but each color class V i satisfies some condition depending on i. Such a coloring is acyclic if th

Oriented list colorings of graphs

✍ Zs. Tuza; M. Voigt 📂 Article 📅 2001 🏛 John Wiley and Sons 🌐 English ⚖ 159 KB 👁 1 views

A 2-assignment on a graph G (V,E) is a collection of pairs Lv of allowed colors speci®ed for all vertices v PV. The graph G (with at least one edge) is said to have oriented choice number 2 if it admits an orientation which satis®es the following property: For every 2-assignment there exists a choic

(2 + ?)-Coloring of planar graphs with l

(2 + ?)-Coloring of planar graphs with large odd-girth

✍ Klostermeyer, William; Zhang, Cun Quan 📂 Article 📅 2000 🏛 John Wiley and Sons 🌐 English ⚖ 258 KB 👁 2 views

The odd-girth of a graph is the length of a shortest odd circuit. A conjecture by Pavol Hell about circular coloring is solved in this article by showing that there is a function f ( ) for each : 0 < < 1 such that, if the odd-girth of a planar graph G is at least f ( ), then G is (2 + )-colorable. N

On 3-colorable non-4-choosable planar gr

On 3-colorable non-4-choosable planar graphs

✍ Voigt, M.; Wirth, B. 📂 Article 📅 1997 🏛 John Wiley and Sons 🌐 English ⚖ 72 KB 👁 2 views

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

On total 9-coloring planar graphs of max

On total 9-coloring planar graphs of maximum degree seven

✍ Sanders, Daniel P.; Zhao, Yue 📂 Article 📅 1999 🏛 John Wiley and Sons 🌐 English ⚖ 202 KB 👁 2 views

Given a graph G, a total k-coloring of G is a simultaneous coloring of the vertices and edges of G with at most k colors. If ∆(G) is the maximum degree of G, then no graph has a total ∆-coloring, but Vizing conjectured that every graph has a total (∆ + 2)-coloring. This Total Coloring Conjecture rem