Induced-Universal Graphs for Graphs with Bounded Maximum Degree
β Scribed by Steve Butler
- Publisher
- Springer Japan
- Year
- 2009
- Tongue
- English
- Weight
- 213 KB
- Volume
- 25
- Category
- Article
- ISSN
- 0911-0119
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
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
Truszczydski, M., Decompositions of graphs into forests with bounded maximum degree, Discrete Mathematics 98 (1991) 207-222.
The total interval number of an n-vertex graph with maximum degree β is at most (β+1/β)n/2, with equality if and only if every component of the graph is K β,β . If the graph is also required to be connected, then the maximum is βn/2 + 1 when β is even, but when β is odd it exceeds [β + 1/(2.5β + 7.7