We study a dynamically evolving random graph which adds vertices and edges using preferential attachment and is “attacked by an adversary”. At time t, we add a new vertex xt a...
In [13], Erd˝os et al. defined the local chromatic number of a graph as the minimum number of colors that must appear within distance 1 of a vertex. For any ∆ ≥ 2, there are ...
Given a graph G = (V, E) with n vertices, m edges and maximum vertex degree ∆, the load distribution of a coloring ϕ : V → {red, blue} is a pair dϕ = (rϕ, bϕ), where rϕ i...
Nitin Ahuja, Andreas Baltz, Benjamin Doerr, Ales P...
We present an improved average case analysis of the maximum cardinality matching problem. We show that in a bipartite or general random graph on n vertices, with high probability ...
Let I be a random 3CNF formula generated by choosing a truth assignment for variables x1, . . . , xn uniformly at random and including every clause with i literals set true by w...