It is shown that if G and H are arbitrary fixed graphs and n is sufficiently large, then Also, we prove that r ( K 1 +F, K,) 5 (m+o(l))&(n -+ GO) for any forest Fwhose largest component has m edges. Thus r(Fe, K,) 5 (1 + o(l))&, where Fe = K1 + CK2. We conjecture that r(Fe, K,) -&(n + cm).
Scattering number in graphs
β Scribed by Shenggui Zhang; Ziguo Wang
- Publisher
- John Wiley and Sons
- Year
- 2001
- Tongue
- English
- Weight
- 75 KB
- Volume
- 37
- Category
- Article
- ISSN
- 0028-3045
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
We investigate the relation between the multichromatic number (discussed by Stahl and by Hilton, Rado and Scott) and the star chromatic number (introduced by Vince) of a graph. Denoting these by Ο \* and Ξ· \* , the work of the above authors shows that Ο \* (G) = Ξ· \* (G) if G is bipartite, an odd cy
GyΓ‘rfΓ‘s and Sumner independently conjectured that for every tree T and integer k there is an integer f (k, T ) such that every graph G with Ο(G) > f(k, t) contains either K k or an induced copy of T . We prove a `topologicalΒ΄version of the conjecture: for every tree T and integer k there is g(k, T )
We introduce in this paper the notion of the chromatic number of an oriented graph G (that is of an antisymmetric directed graph) defined as the minimum order of an oriented graph H such that G admits a homomorphism to H. We study the chromatic number of oriented k-trees and of oriented graphs with
This note proves that the game chromatic number of an outerplanar graph is at most 7. This improves the previous known upper bound of the game chromatic number of outerplanar graphs.