Homomorphisms and edge-colourings of planar graphs
β Scribed by Reza Naserasr
- Book ID
- 108167416
- Publisher
- Elsevier Science
- Year
- 2007
- Tongue
- English
- Weight
- 136 KB
- Volume
- 97
- Category
- Article
- ISSN
- 0095-8956
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
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
It is proved that if G is a planar graph with total (vertex-edge) chromatic number Ο , maximum degree and girth g, then Ο = + 1 if β₯ 5 and g β₯ 5, or β₯ 4 and g β₯ 6, or β₯ 3 and g β₯ 10. These results hold also for graphs in the projective plane, torus and Klein bottle.