Let IGI be the number of vertices of a graph G and to(G) be the density of G. We call a graph G packed if the clique graph K(G) of G has exactly 2 IGI-O'(G) cliques. We correct the characterization of clique graphs of packed graphs given in Theorem 3.2 of Hedman [3]. All graphs considered here are f
Topological cliques of random graphs
β Scribed by B Bollobas; P.A Catlin
- Publisher
- Elsevier Science
- Year
- 1981
- Tongue
- English
- Weight
- 186 KB
- Volume
- 30
- Category
- Article
- ISSN
- 0095-8956
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π SIMILAR VOLUMES
We consider the following probabilistic model of a graph on n labeled vertices. ## Ε½ . First choose a random graph G n, 1r2 , and then choose randomly a subset Q of vertices of size k and force it to be a clique by joining every pair of vertices of Q by an edge. The problem is to give a polynomia
For each natural number n, denote by G(n) the set of all numbers c such that there exists a graph with exactly c cliques (i.e., complete subgraphs) and n vertices. We prove the asymptotic estimate Ia(n)l = 0(2"n -z/5) and show that all natural numbers between n + 1 and 2 "-6"5~6 belong to G(n). Thus
## Abstract The clique graph __K__(__G__) of a graph is the intersection graph of maximal cliques of __G.__ The iterated clique graph __K__^__n__^(__G__) is inductively defined as __K__(K^nβ1^(__G__)) and __K__^1^(__G__) = __K__(__G__). Let the diameter diam(__G__) be the greatest distance between