AbstractLet G(n, p) be a graph on n vertices in which each possible edge is presented independently with probability p=p(n) and v1(n, p) denote the number of vertices of degree 1 in G(n, p). It is shown that if ε > 0 and np(n)→∞ then the probability that G(n, p) contains cycles of all lengths r, 3⩽r⩽n−(1+ε)v1(n,p), tends to 1 as n→∞
AbstractLet r be any integer ≥2. There exist absolute constants C1 and C2 such that if G(N, p) denot...
Abstract. Consider a random multigraph G ∗ with given vertex degrees d1,..., dn, contructed by the c...
Consider random regular graphs of order n and degree d = d(n) ≥ 3. Let g = g(n) ≥ 3 satisfy (d-1)2g-...
AbstractLet G(n, p) be a graph on n vertices in which each possible edge is presented independently ...
For a given graph G of minimum degree at least k, let Gp denote the random spanning subgraph of G ob...
For a given graph G of minimum degree at least k, let Gp denote the random spanning subgraph of G ob...
Abstract. Let H be a given finite (possibly empty) family of connected graphs, each containing a cyc...
Over 50 years ago, Erdős and Gallai conjectured that the edges of every graph on n vertices can be d...
AbstractPósa proved that a random graph with cn log n edges is Hamiltonian with probability tending ...
Let G be any graph of minimum degree at least k, and let Gp be the random subgraph of G obtained by ...
Let G3−out denote the random graph on vertex set [n] in which each vertex chooses 3 neighbors unifor...
We consider random subgraphs of a fixed graph G = (V,E) with large minimum degree. We fix a positive...
This paper concerns the degree sequence d1 ≥ d2 ≥ … ≥ dn of a randomly labeled graph of order n in w...
The probability that a random labelled r-regular graph contains a given number of cycles of given le...
AbstractLet H(n, p) denote the size of the largest induced cycle in a random graph G(n, p). It is sh...
AbstractLet r be any integer ≥2. There exist absolute constants C1 and C2 such that if G(N, p) denot...
Abstract. Consider a random multigraph G ∗ with given vertex degrees d1,..., dn, contructed by the c...
Consider random regular graphs of order n and degree d = d(n) ≥ 3. Let g = g(n) ≥ 3 satisfy (d-1)2g-...
AbstractLet G(n, p) be a graph on n vertices in which each possible edge is presented independently ...
For a given graph G of minimum degree at least k, let Gp denote the random spanning subgraph of G ob...
For a given graph G of minimum degree at least k, let Gp denote the random spanning subgraph of G ob...
Abstract. Let H be a given finite (possibly empty) family of connected graphs, each containing a cyc...
Over 50 years ago, Erdős and Gallai conjectured that the edges of every graph on n vertices can be d...
AbstractPósa proved that a random graph with cn log n edges is Hamiltonian with probability tending ...
Let G be any graph of minimum degree at least k, and let Gp be the random subgraph of G obtained by ...
Let G3−out denote the random graph on vertex set [n] in which each vertex chooses 3 neighbors unifor...
We consider random subgraphs of a fixed graph G = (V,E) with large minimum degree. We fix a positive...
This paper concerns the degree sequence d1 ≥ d2 ≥ … ≥ dn of a randomly labeled graph of order n in w...
The probability that a random labelled r-regular graph contains a given number of cycles of given le...
AbstractLet H(n, p) denote the size of the largest induced cycle in a random graph G(n, p). It is sh...
AbstractLet r be any integer ≥2. There exist absolute constants C1 and C2 such that if G(N, p) denot...
Abstract. Consider a random multigraph G ∗ with given vertex degrees d1,..., dn, contructed by the c...
Consider random regular graphs of order n and degree d = d(n) ≥ 3. Let g = g(n) ≥ 3 satisfy (d-1)2g-...
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