๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

Representing Groups by Colourings of Graphs

โœ Scribed by Ulrike Baumann


Publisher
John Wiley and Sons
Year
1997
Tongue
English
Weight
297 KB
Volume
188
Category
Article
ISSN
0025-584X

No coin nor oath required. For personal study only.


๐Ÿ“œ SIMILAR VOLUMES


Representation of Permutation Groups by
โœ Ulrike Baumann ๐Ÿ“‚ Article ๐Ÿ“… 2006 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 432 KB

## Abstract The topic of this paper is representing permutation groups by connected graphs with proper edge colourings. Every connected graph __G__ with a proper edge colouring ฯ• determines a group __A~c~__(__G__, ฯ•) of graph automorphisms which preserve the colours of the edges. We characterize pe

Symmetry Groups of Coloured Graphs
โœ Ulrike Baumann ๐Ÿ“‚ Article ๐Ÿ“… 1993 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 474 KB

## Abstract A perfect colouring ฮฆ of a simple undirected connected graph __G__ is an edge colouring such that each vertex is incident with exactly one edge of each colour. This paper concerns the problem of representing groups by graphs with perfect colourings. We define groups of graph automorphis

Total Colourings of Planar Graphs with L
โœ O.V. Borodin; A.V. Kostochka; D.R. Woodall ๐Ÿ“‚ Article ๐Ÿ“… 1998 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 96 KB

It is proved that if G is a planar graph with total (vertex-edge) chromatic number ฯ‡ , maximum degree and girth g, then ฯ‡ = + 1 if โ‰ฅ 5 and g โ‰ฅ 5, or โ‰ฅ 4 and g โ‰ฅ 6, or โ‰ฅ 3 and g โ‰ฅ 10. These results hold also for graphs in the projective plane, torus and Klein bottle.

Circular Colouring and Orientation of Gr
โœ Xuding Zhu ๐Ÿ“‚ Article ๐Ÿ“… 2002 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 88 KB

This paper proves that if a graph G has an orientation D such that for each cycle C with djCj รฐmod kรž 2 f1; 2; . . . ; 2d ร€ 1g we have jCj=jC รพ j4k=d and jCj=jC ร€ j4k=d; then G has a รฐk; dรž-colouring and hence w c รฐGรž4k=d: This is a generalization of a result of Tuza (J. Combin. Theory Ser. B 55 (19

Automorphism Groups of Covering Graphs
โœ Norbert Seifter; Vladimir I. Trofimov ๐Ÿ“‚ Article ๐Ÿ“… 1997 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 226 KB

For a large class of finite Cayley graphs we construct covering graphs whose automorphism groups coincide with the groups of lifted automorphisms. As an application we present new examples of 1ร‚2-transitive and 1-regular graphs.

Representing the Quotient Groups of a Fi
โœ Derek F. Holt; Jacqueline Walton ๐Ÿ“‚ Article ๐Ÿ“… 2002 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 207 KB

Let G be a permutation group of finite degree d. We prove that the product of the orders of the composition factors of G that are not alternating groups acting naturally, in a sense that will be made precise, is bounded by c d-1 /d, where c = 4 5. We use this to prove that any quotient G/N of G has