Cycles in sparse random graphs
โ Scribed by Marinari, E; Kerrebroeck, V V
- Book ID
- 120936201
- Publisher
- Institute of Physics
- Year
- 2008
- Tongue
- English
- Weight
- 442 KB
- Volume
- 95
- Category
- Article
- ISSN
- 1742-6588
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
Let k be a fixed positive integer. A graph H has property Mk if it contains [ยฝk] edge disjoint hamilton cycles plus a further edge disjoint matching which leaves at most one vertex isolated, if k is odd. Let p = c/n, where c is a large enough constant. We show that G,,p a.s. contains a vertex induce
Let G n,m,k denote the space of simple graphs with n vertices, m edges, and minimum degree at least k, each graph G being equiprobable. Let G have property A k , if G contains (k -1)/2 edge disjoint Hamilton cycles, and, if k is even, a further edge disjoint matching of size n/2 . We prove that, for
tuczak, T., Cycles in random graphs, Discrete Mathematics 98 (1991) 231-236. Let G(n, p) be a graph on n vertices in which each possible edge is presented independently with probability p = p(n) and u'(n, p) denote the number of vertices of degree 1 in G(n, p). It is shown that if E > 0 and rip(n)))