Erdos posed the problem of finding conditions on a graph G that imply t(G) = b(G), where t(G) is the largest number of edges in a triangle-free subgraph and b(G) is the largest nu...
The bandwidth minimization problem has a long history and a number of practical applications. In this paper we introduce a natural extension of bandwidth to partially ordered layo...
Let T be the Cayley graph of a finitely generated free group F. Given two vertices in T consider all the walks of a given length between these vertices that at a certain time must...
We give a new upper bound for the rectilinear crossing number cr(n) of the complete geometric graph Kn. We prove that cr(n) ≤ 0.380559 ¡n 4 ¢ + Θ(n3 ) by means of a new const...
We consider the extension of the last-in-first-out graph searching game of Giannopoulou and Thilikos to digraphs. We show that all common variations of the game require the same ...