Denote the number of vertices of G by ]G[. A clique of graph G is a maximal complete subgraph. The density oJ(G) is the number of vertices in the largest clique of G. If Β’o(G)>~Β½ ]GI, then G has at most 2 tΒ°l-'cG) cliques. The extremal graphs are then examined as wen. ## Terminology We will be co
The maximum number of q-cliques in a graph with no p-clique
β Scribed by Steven Roman
- Publisher
- Elsevier Science
- Year
- 1976
- Tongue
- English
- Weight
- 805 KB
- Volume
- 14
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
Let G be a line graph. Orlin determined the clique covering and clique partition numbers cc(G) and cp(G). We obtain a constructive proof of Orlin's result and in doing so we are able to completely enumerate the number of distinct minimal clique covers and partitions of G, in terms of easily calculab
Chvatal established that r(T,, K,,) = (m -1 ) ( n -1 ) + 1, where T, , , is an arbitrary tree of order m and K, is the complete graph of order n. This result was extended by Chartrand, Gould, and Polimeni who showed K, could be replaced by a graph with clique number n and order n + 5 provided n 2 3
The following problem is investigated. Given an undirected graph G, determine the smallest cardinality of a vertex set that meets all complete subgraphs KC G maximal under inclusion.