We consider a random subgraph Gp of a host graph G formed by retaining each edge of G with probability p. We address the question of determining the critical value p (as a function...
: Let G be a graph with maximum degree d ≥ 3 and ω(G) ≤ d, where ω(G) is the clique number of the graph G. Let p1 and p2 be two positive integers such that d = p1 + p2. In th...
The main aim of this short paper is to answer the following question. Given a fixed graph H, for which values of the degree d does a random d-regular graph on n vertices contain ...
This paper addresses the following questions for a given tree T and integer d 2: (1) What is the minimum number of degree-d subtrees that partition E(T)? (2) What is the minimum n...
Widely varying node degrees occur in software dependency graphs, hyperlink structures, social networks, and many other real-world graphs. Finding dense subgraphs in such graphs is ...