The recursive computation of the interlace polynomial introduced by Arratia, Bollobás and Sorkin is defined in terms of a new pivoting operation on undirected simple graphs. In this paper, we interpret the new pivoting operation on graphs in terms of standard pivoting (on matrices). Specifically, we show that, up to swapping vertex labels, Arratia et al.’s pivoting operation on a graph is equiv...

In previous papers, Catlin introduced four functions, denoted S, S, S , and S , between sets of nite graphs. These functions proved to be very useful in establishing properties of several classes of graphs, including supereulerian graphs and graphs with nowhere zero kows for a xed integer k¿ 3. Unfortunately, a subtle error caused several theorems previously published in Catlin (Discrete Math. ...

We further study the effect of odd cycle inequalities in the description of the polytopes associated with the p-median and uncapacitated facility location problems. We show that the obvious integer linear programming formulation together with the odd cycle inequalities completely describe these polytopes for the class of restricted Y-graphs. This extends our results for the class of Y-free grap...

For the earliest arrival flow problem one is given a network G = (V,A) with capacities u(a) and transit times τ(a) on its arcs a ∈ A, together with a source and a sink vertex s, t ∈ V . The objective is to send flow from s to t that moves through the network over time, such that for each point in time θ ∈ [0, T ) the maximum possible amount of flow reaches t. If, for each θ ∈ [0, T ) this flow ...

We study the separation of TCP flows into short lived and long lived ones, and the subsequent allocation of bandwidth to reflect the dynamically changing load due to short lived flow fluctuations. Three schemes are presented to assist in determining and allocating the bandwidth to short lived flows. Each one represents a different compromise in terms of state and execution complexity. However, ...

A set A of vertices of a graph G is called d-scattered in G if no two d-neighborhoods of (distinct) vertices of A intersect. In other words, A is d-scattered if no two distinct vertices of A have distance at most 2d. This notion was isolated in the context of finite model theory by Gurevich and recently it played a prominent role in the study of homomorphism preservation theorems for special cl...

Marginal AMP chain graphs are a recently introduced family of models that is based on graphs that may have undirected, directed and bidirected edges. They unify and generalize the AMP and the multivariate regression interpretations of chain graphs. In this paper, we present a constraint based algorithm for learning a marginal AMP chain graph from a probability distribution which is faithful to ...