In their paper on the "chasm at depth four", Agrawal and Vinay have shown that polynomials in m variables of degree O(m) which admit arithmetic circuits of size 2o(m) al...
In the minimum sum edge coloring problem, we aim to assign natural numbers to edges of a graph, so that adjacent edges receive different numbers, and the sum of the numbers assign...
Jean Cardinal, Vlady Ravelomanana, Mario Valencia-...
Let G be a minimally k-connected graph with n nodes and m edges. Mader proved that if n 3k - 2 then m k(n - k), and for n 3k - 1 an equality is possible if, and only if, G is t...
We use large deviations to prove a general theorem on the asymptotic edge-weighted height Hn of a large class of random trees for which Hn c log n for some positive constant c. A...
Abstract. Let G denote a directed graph with adjacency matrix Q and indegree matrix D. We consider the Kirchhoff matrix L = D - Q, sometimes referred to as the directed Laplacian. ...