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RSA
2011
13 years 7 days ago
2011
An old problem of Erd˝os, Fajtlowicz and Staton asks for the order of a largest induced regular subgraph that can be found in every graph on n vertices. Motivated by this problem...
RSA
2011
13 years 7 days ago
2011
: The classical result in the theory of random graphs, proved by Erd˝os and Rényi in 1960, concerns the threshold for the appearance of the giant component in the random graph pr...
RSA
2011
12 years 8 months ago
2011
We consider a conditioned Galton–Watson tree and prove an estimate of the number of pairs of vertices with a given distance, or, equivalently, the number of paths of a given leng...
RSA
2011
13 years 7 days ago
2011
Determining the cardinality and describing the structure of H-free graphs is wellinvestigated for many graphs H. In the nineties, Prömel and Steger proved that for a graph H with...
RSA
2011
13 years 7 days ago
2011
We prove that for fixed integer D and positive reals α and γ, there exists a constant C0 such that for all p satisfying p(n) ≥ C0/n, the random graph G(n, p) asymptotically a...