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Set colourings of graphs

✍ Scribed by Béla Bollobás; Andrew Thomason

Publisher
Elsevier Science
Year
1979
Tongue
English
Weight
584 KB
Volume
25
Category
Article
ISSN
0012-365X

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📜 SIMILAR VOLUMES

List colourings of planar graphs
List colourings of planar graphs
✍ Margit Voigt 📂 Article 📅 1993 🏛 Elsevier Science 🌐 English ⚖ 259 KB

A graph G = G( V, E) is called L-list colourable if there is a vertex colouring of G in which the colour assigned to a vertex u is chosen from a list L(v) associated with this vertex. We say G is k-choosable if all lists L(u) have the cardinality k and G is L-list colourable for all possible assignm

Total Colourings of Planar Graphs with L
Total Colourings of Planar Graphs with Large Girth
✍ O.V. Borodin; A.V. Kostochka; D.R. Woodall 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 96 KB

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

A new upper bound for total colourings o
A new upper bound for total colourings of graphs
✍ Abdón Sánchez-Arroyo 📂 Article 📅 1995 🏛 Elsevier Science 🌐 English ⚖ 118 KB

We give a new upper bound on the total chromatic number of a graph. This bound improves the results known for some classes of graphs. The bound is stated as follows: ZT ~< Z~ + L l3 ~ J + 2, where Z is the chromatic number, Z~ is the edge chromatic number (chromatic index) and ZT is the total chroma

Graphs which have n/2-minimal line-disti
Graphs which have n/2-minimal line-distinguishing colourings
✍ B.E. Brunton; B.J. Wilson; T.S. Griggs 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 436 KB

A graph G is said to be k-MLD-colourable if G possesses a k-vertex colouring such that each pair ofcolours appears on precisely one edge of G. Given G with n vertices and valency sequence S which is n/2-MLD-colourable it is shown how any other graph on n vertices with valency sequence S can be obtai

Symmetry Groups of Coloured Graphs
Symmetry Groups of Coloured Graphs
✍ Ulrike Baumann 📂 Article 📅 1993 🏛 John Wiley and Sons 🌐 English ⚖ 474 KB

## Abstract A perfect colouring Φ 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