𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Dirac's map-color theorem for choosability

✍ Scribed by B�hme, T.; Mohar, B.; Stiebitz, M.

Publisher
John Wiley and Sons
Year
1999
Tongue
English
Weight
290 KB
Volume
32
Category
Article
ISSN
0364-9024

No coin nor oath required. For personal study only.

✦ Synopsis

It is proved that the choice number of every graph G embedded on a surface of Euler genus ε ≥ 1 and ε = 3 is at most the Heawood number H(ε) = (7 + √ 24ε + 1)/2 and that the equality holds if and only if G contains the complete graph K H(ε) as a subgraph.

📜 SIMILAR VOLUMES

The last excluded case of Dirac's map-co
The last excluded case of Dirac's map-color theorem for choosability
✍ Daniel Král'; Riste S̆krekovski 📂 Article 📅 2006 🏛 John Wiley and Sons 🌐 English ⚖ 294 KB

## Abstract In 1890, Heawood established the upper bound $H ( \varepsilon )= \left \lfloor 7+\sqrt {24\varepsilon +1}/{2}\right \rfloor$ on the chromatic number of every graph embedded on a surface of Euler genus ε ≥ 1. Almost 80 years later, the bound was shown to be tight by Ringel and Youngs. Th

An L2-Index Theorem for Dirac Operators
An L2-Index Theorem for Dirac Operators on S1×R3
✍ Tom M.W. Nye; Michael A. Singer 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 178 KB

An expression is found for the L 2 -index of a Dirac operator coupled to a connection on a U n vector bundle over S 1 \_R 3 . Boundary conditions for the connection are given which ensure the coupled Dirac operator Fredholm. Callias' index theorem is used to calculate the index when the connection i

A dual-color FISH framework map for the
A dual-color FISH framework map for the characterization of the Sai1 tumor suppression region on rat chromosome 5
✍ Khalil Helou; Xu Chun Lü; Kerstin Montelius-Alatalo; Fredrik Ståhl; Karin Klinga 📂 Article 📅 2000 🏛 John Wiley and Sons 🌐 English ⚖ 307 KB

The analysis of cell hybrids between malignant mouse hepatoma cells and normal rat fibroblasts has previously demonstrated the critical role of a deletion in rat chromosome 5 (RNO5) that was related to an anchorage independent phenotype. Those hybrids that were anchorage independent displayed loss o