SparseH-Colourable Graphs of Bounded Maximum Degree
β Scribed by Hossein Hajiabolhassan; Xuding Zhu
- Publisher
- Springer Japan
- Year
- 2004
- Tongue
- English
- Weight
- 312 KB
- Volume
- 20
- Category
- Article
- ISSN
- 0911-0119
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
Truszczydski, M., Decompositions of graphs into forests with bounded maximum degree, Discrete Mathematics 98 (1991) 207-222.
For graphs G and H we write G wΓ ind H if every 2-edge colouring of G yields an induced monochromatic copy of H. The induced Ramsey number for H is defined as r ind (H)=min[ |V(G)|: G wΓ ind H]. We show that for every d 1 there exists an absolute constant c d such that r ind (H n, d ) n cd for every
A graph is 2K,-free if it does not contain an independent pair of edges as an induced subgraph. We show that if G is 2K,-free and has maximum degree A(G) = D, then G has at most 5D2/4 edges if D is even. If D is odd, this bound can be improved to (5D\* -20 + 1)/4. The extremal graphs are unique.
## Abstract We prove results on partitioning graphs __G__ with bounded maximum degree. In particular, we provide optimal bounds for bipartitions __V__(__G__) = __V__~1~ βͺ __V__~2~ in which we minimize {__e__(__V__~1~), __e__(__V__~2~)}. Β© 2004 Wiley Periodicals, Inc. J Graph Theory 46: 131β143, 200