For a positive integer k, a k-rainbow dominating function of a graph G is a function f from the vertex set V (G) to the set of all subsets of the set {1, 2, . . . , k} such that for any vertex rainbow dominating family (of functions) on G. The maximum number of functions in a k-rainbow dominating f
On the Nordhaus-Gaddum Problem for the k-Defective Chromatic Number of a Graph
β Scribed by Nirmala Achuthan N. R. Achuthan; M. Simanihuruk
- Publisher
- Elsevier Science
- Year
- 2003
- Tongue
- English
- Weight
- 201 KB
- Volume
- 15
- Category
- Article
- ISSN
- 1571-0653
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
Stiebitz, M., On Hadwiger's number-A problem of the Nordhaus-Gaddum type, Discrete Mathematics 101 (1992) 307-317. The Hadwiger number of a graph G = (V, E), denoted by q(G), is the maximum size of a complete graph to which G can be contracted. Let %((n, k):= {G 1 IV(G)1 = n and n(G) = k}. We shall
We characterize the graphs G such that Ch(G) + Ch( G) = n + 1, where Ch(G) is the choice number (list-chromatic number) of G and n is its number of vertices.
The harmonious chromatic number of a graph G, denoted by h(G), is the least number of colon which can be assigned to the vertices of G such that adjacent vertices are colored differently and any two distinct edges have different color pairs. This is a slight variation of a definition given independe
We give an upper bound on the chromatic number of a graph in terms of its maximum degree and the size of the largest complete subgraph. Our result extends a theorem due to i3rook.s.