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...
Michael Krivelevich, Benny Sudakov, Nicholas C. Wo...
In this paper, we prove that there exists a function k = (4 + o(1))k such that G(n, /n) contains a k-regular graph with high probability whenever > k. In the case of k = 3, it...
Given an undirected graph G = (V, E) with a set V of vertices and a set E of edges, the graph coloring problem consists of partitioning all vertices into k independent sets and th...
Given a vector ( 1 2 ::: t) of non increasing positive integers, and an undirected graph G = (V E), an L( 1 2 ::: t)-coloring of G is a function f from the vertex set V to a set o...
Alan A. Bertossi, Maria Cristina Pinotti, Romeo Ri...
The preferential attachment graph Gm(n) is a random graph formed by adding a new vertex at each time step, with m edges which point to vertices selected at random with probability...