𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Total chromatic number of graphs with small genus

✍ Scribed by Rong Luo; Cun-Quan Zhang

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
338 KB
Volume
11
Category
Article
ISSN
1571-0653

No coin nor oath required. For personal study only.

πŸ“œ SIMILAR VOLUMES

Maximum genus and chromatic number of gr
Maximum genus and chromatic number of graphs
✍ Yuanqiu Huang πŸ“‚ Article πŸ“… 2003 πŸ› Elsevier Science 🌐 English βš– 157 KB

Let T be a spanning tree of a connected graph G. Denote by (G; T ) the number of components in G\E(T ) with odd number of edges. The value minT (G; T ) is known as the Betti deΓΏciency of G, denoted by (G), where the minimum is taken over all spanning trees T of G. It is known (N.H. Xuong, J. Combin.

Small graphs with chromatic number 5: A
Small graphs with chromatic number 5: A computer search
✍ Tommy Jensen; Gordon F. Royle πŸ“‚ Article πŸ“… 1995 πŸ› John Wiley and Sons 🌐 English βš– 402 KB

## Abstract In this article we give examples of a triangle‐free graph on 22 vertices with chromatic number 5 and a __K__~4~‐free graph on 11 vertices with chromatic number 5. We very briefly describe the computer searches demonstrating that these are the smallest possible such graphs. All 5‐critica

Total chromatic number of planar graphs
Total chromatic number of planar graphs with maximum degree ten
✍ Weifan Wang πŸ“‚ Article πŸ“… 2006 πŸ› John Wiley and Sons 🌐 English βš– 161 KB πŸ‘ 1 views

## Abstract In this article we prove that the total chromatic number of a planar graph with maximum degree 10 is 11. Β© 2006 Wiley Periodicals, Inc. J Graph Theory 54: 91–102, 2007

Total chromatic number of complete r-par
Total chromatic number of complete r-partite graphs
✍ K. H. Chew; H. P. Yap πŸ“‚ Article πŸ“… 1992 πŸ› John Wiley and Sons 🌐 English βš– 284 KB πŸ‘ 1 views

## Abstract Rosenfeld (1971) proved that the Total Colouring Conjecture holds for balanced complete __r__‐partite graphs. Bermond (1974) determined the exact total chromatic number of every balanced complete __r__‐partite graph. Rosenfeld's result had been generalized recently to complete __r__‐par

The vertex-face total chromatic number o
The vertex-face total chromatic number of Halin graphs
✍ Lam, Peter C. B.; Zhang, Zhongfu πŸ“‚ Article πŸ“… 1997 πŸ› John Wiley and Sons 🌐 English βš– 69 KB πŸ‘ 2 views

In this paper, we shall first prove that for a Halin graph G, 4 Β°xT (G) Β°6, where x T (G) is the vertex-face total chromatic number of G. Second, we shall establish a sufficient condition for a Halin graph to have a vertex-face total chromatic number of 6. Finally, we shall give a necessary and suff