A d-regular graph has largest or first (adjacency matrix) eigenvalue 1 = d. In this paper we show the following conjecture of Alon. Fix an integer d > 2 and a real > 0. Then...
This work addresses the problem of computing a certified ǫ-approximation of all real roots of a square-free integer polynomial. We proof an upper bound for its bit complexity, b...
A k-separated matching in a graph is a set of edges at distance at least k from one another (hence, for instance, a 1-separated matching is just a matching in the classical sense)...
For a bounded integer , we wish to color all edges of a graph G so that any two edges within distance have different colors. Such a coloring is called a distance-edge-coloring or ...
Abstract. A strong vertex coloring of a hypergraph assigns distinct colors to vertices that are contained in a common hyperedge. This captures many previously studied graph colorin...