This paper concerns vertex connectivity in random graphs. We present results bounding the cardinality of the biggest k-block in random graphs of the G,~p model, for any constant value of k. Our results extend the work of Erd6s and R6nyi and Karp and Tarjan. We prove here that (~.~p, with [9 ~ tin, h
On rainbow-k-connectivity of random graphs
โ Scribed by Jing He; Hongyu Liang
- Book ID
- 113663329
- Publisher
- Elsevier Science
- Year
- 2012
- Tongue
- English
- Weight
- 149 KB
- Volume
- 112
- Category
- Article
- ISSN
- 0020-0190
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๐ SIMILAR VOLUMES
We prove that, in a random graph with n vertices and N = cn log n edges, the subgraph generated by a set of all vertices of degree at least k + 1 is k-leaf connected for c > f . A threshold function for k-leaf connectivity is also found. ## 1. MAIN RESULTS Let G = (V(G),E(G)) be a graph, where V (
For n points uniformly randomly distributed on the unit cube in d dimensions, ## ลฝ . with dG 2, let respectively, denote the minimum r at which the graph, obtained by n n adding an edge between each pair of points distant at most r apart, is k-connected ลฝ . w x respectively, has minimum degree k