We address the problem of nding a minimal separator in a di rected acyclic graph DAG namely nding a set Z of nodes that d separates a given pair of nodes such that no proper subset of Z d separates that pair We analyze several versions of this problem and o er polynomial algorithms for each These include nding a minimal separator from a restricted set of nodes nding a minimum cost separator and...

String graphs, that is, intersection graphs of curves in the plane, have been studied since the 1960s. We provide an expository presentation of several results, including very recent ones: some string graphs require an exponential number of crossings in every string representation; exponential number is always sufficient; string graphs have small separators; and the current best bound on the cr...

I present an efficient algorithm which lists the minimal separators of a planar graph in O(n) per separator.

For real numbers c, ε > 0, let Gc,ε denote the class of graphs G such that each subgraph H of G has a balanced separator of order at most c|V (H)|1−ε. A class G of graphs has strongly sublinear separators if G ⊆ Gc,ε for some c, ε > 0. We investigate properties of such graph classes, leading in particular to an approximate algorithm to determine membership in Gc,ε: there exist c > 0 such that f...

We propose a graph-based decomposition methodology of a network of document features represented by a terminology graph. The graph is automatically extracted from raw data based on Natural Language Processing techniques implemented in the TermWatch system. These graphs are Small Worlds. Based on clique minimal separators and the associated graph of atoms: a subgraph without clique separator, we...

Microbial fuel cells (MFCs) with hydrophilic poly(vinyl alcohol) (PVA) separators showed higher Coulombic efficiencies (94%) and power densities (1220 mW m(-2)) than cells with porous glass fiber separators or reactors without a separator after 32 days of operation. These remarkable increases in both the coublomic efficiency and the power production of the microbial fuel cells were made possibl...

This paper describes the fabrication of novel modified polyethylene (PE) membranes using plasma technology to create high-performance and cost-effective separator membranes for practical applications in lithium-ion polymer batteries. The modified PE membrane via plasma modification process plays a critical role in improving wettability and electrolyte retention, interfacial adhesion between sep...

In this report, we present the intersection graphs and describe the role they play in computations of treewidth. We introduce minimal triangulations, minimal separators, potential maximal cliques and blocks as the main tools for exact computation and approximation of that important graph parameter. The first chapter is an introduction to the intersection graph theory. We give all the necessary ...

A k-queue layout of a graph consists of a total order of the vertices, and a partition of the edges into k sets such that no two edges that are in the same set are nested with respect to the vertex ordering. A k-track layout of a graph consists of a vertex kcolouring, and a total order of each vertex colour class, such that between each pair of colour classes no two edges cross. The queue-numbe...

We present O(n’R + n3R3) time algorithms to compute the treewidth, pathwidth, minimum fill-in and minimum interval graph completion of asteroidal triple-free graphs, where n is the number of vertices and R is the number of minimal separators of the input graph. This yields polynomial time algorithms for the four NP-complete graph problems on any subclass of the asteroidal triple-free graphs tha...