The oriented chromatic number Ο o ( G) of an oriented graph G = (V, A) is the minimum number of vertices in an oriented graph H for which there exists a homomorphism of G to H. The oriented chromatic number Ο o (G) of an undirected graph G is the maximum of the oriented chromatic numbers of all the
Acyclic orientations of a graph and chromatic and independence numbers
β Scribed by R.W Deming
- Publisher
- Elsevier Science
- Year
- 1979
- Tongue
- English
- Weight
- 614 KB
- Volume
- 26
- Category
- Article
- ISSN
- 0095-8956
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
Sampathkumar, E., Generalizations of independence and chromatic numbers of a graph, Discrete Mathematics 115 (1993) 2455251. Let G = (V, E) be a graph and k > 2 be an integer. A set S c V is k-independent if every component in the subgraph (S) induced by S has order at most k-1. The general chromati
## Abstract Star chromatic number, introduced by A. Vince, is a natural generalization of chromatic number. We consider the question, βWhen is Ο\* < Ο?β We show that Ο\* < Ο if and only if a particular digraph is acyclic and that the decisioin problem associated with this question is probably not i
The local independence number i (G) of a graph G at a distance i is the maximum number of independent vertices at distance i from any vertex. We study the impact of restricting i (G) on the (global) independence number (G). Among others, we show that in graphs with bounded diameter, (G) is bounded i
It was proved (A. Kotlov and L. LovΓ‘sz, The rank and size of graphs, J. Graph Theory 23 (1996), 185-189) that the number of vertices in a twin-free graph is O(( β 2) r ) where r is the rank of the adjacency matrix. This bound was shown to be tight. We show that the chromatic number of a graph is o(β
This paper studies circular chromatic numbers and fractional chromatic numbers of distance graphs G(Z , D) for various distance sets D. In particular, we determine these numbers for those D sets of size two, for some special D sets of size three, for