✦ LIBER ✦

Coloring edges of embedded graphs

✍ Scribed by Daniel P. Sanders; Yue Zhao

Publisher: John Wiley and Sons
Year: 2000
Tongue: English
Weight: 80 KB
Volume: 35
Category: Article
ISSN: 0364-9024
DOI: 10.1002/1097-0118(200011)35:3<197::aid-jgt5>3.0.co;2-1

No coin nor oath required. For personal study only.

✦ Synopsis

In this paper, we prove that any graph G with maximum degree ÁG ! 11 p 49À241AEa2, which is embeddable in a surface AE of characteristic 1AE 1 and satis®es jVGj b 2ÁGÀ5À2 p 6ÁG, is class one.

📜 SIMILAR VOLUMES

3-Coloring graphs embedded in surfaces

✍ Zhao, Yue 📂 Article 📅 2000 🏛 John Wiley and Sons 🌐 English ⚖ 66 KB 👁 1 views

In this article, we show that there exists an integer k(Σ)

Optimal edge coloring of large graphs

✍ G�mez, J.; Escudero, M. 📂 Article 📅 1999 🏛 John Wiley and Sons 🌐 English ⚖ 95 KB 👁 2 views

Most of the general families of large considered graphs in the context of the so-called (⌬, D) problem-that is, how to obtain graphs with maximum order, given their maximum degree ⌬ and their diameter D-known up to now for any value of ⌬ and D, are obtained as product graphs, compound graphs, and ge

Properly colored hamilton cycles in edge

Properly colored hamilton cycles in edge-colored complete graphs

✍ N. Alon; G. Gutin 📂 Article 📅 1997 🏛 John Wiley and Sons 🌐 English ⚖ 156 KB 👁 2 views

It is shown that, for ⑀ ) 0 and n ) n ⑀ , any complete graph K on n vertices 0 ' Ž . whose edges are colored so that no vertex is incident with more than 1 y 1r 2 y ⑀ n edges of the same color contains a Hamilton cycle in which adjacent edges have distinct colors. Moreover, for every k between 3 and

An edge coloring problem for graph produ

An edge coloring problem for graph products

✍ Faudree, R. J.; Gy�rf�s, Andr�as; Schelp, R. H. 📂 Article 📅 1996 🏛 John Wiley and Sons 🌐 English ⚖ 315 KB 👁 1 views

The edges of the Cartesian product of graphs G x H a r e to be colored with the condition that all rectangles, i.e., K2 x K2 subgraphs, must be colored with four distinct colors. The minimum number of colors in such colorings is determined for all pairs of graphs except when G is 5-chromatic and H

Embedding of graphs in two-irregular gra

Embedding of graphs in two-irregular graphs

✍ M. Axenovich; Z. Füredi 📂 Article 📅 2001 🏛 John Wiley and Sons 🌐 English ⚖ 90 KB

Construction of uniquelyH-colorable grap

Construction of uniquelyH-colorable graphs

✍ Zhu, Xuding 📂 Article 📅 1999 🏛 John Wiley and Sons 🌐 English ⚖ 190 KB 👁 2 views

We shall prove that for any graph H that is a core, if χ(G) is large enough, then H × G is uniquely H-colorable. We also give a new construction of triangle free graphs, which are uniquely n-colorable.