In this paper we consider the class of simple graphs defined by excluding, as inducedsubgraphs, even holes (i.e. chordless cycles of even length). These graphs are known aseven-hole-free graphs. We prove a decomposition theorem for even-hole-free graphs, thatuses star cutsets and 2-joins. This is a significant strengthening of the only other pre-viously known decomposition of ev...

We investigate the structure of a digraph having a transitive automorphism group where every cutset of minimal cardinality consists of all successors or all predecessors of some vertex. We improve most of the existing results in this area.

GSAT is a randomized greedy local repair procedure that was introduced for solving propositional satisfiability and constraint satisfaction problems. We present an improvement to GSAT that is sensitive to the problem’s structure. When the problem has a tree structure the algorithm is guaranteed to find a solution in linear time. For non-tree networks, the algorithm designates a subset of nodes,...

Finding low elimination trees is important in parallel Cholesky factorization. We look at two orderings for achieving low height, Nested Dissection and Maximal Independent Subset, and show that in general they will not give a minimum height elimination tree. A more general version of Nested Dissection called Minimal Cutset orderings is shown to always contain an ordering that gives a minimum he...

A conjecture concerning perfect graphs asserts that if for a Berge graph G the following three conditions hold: 1. neither G, nor Ḡ has an even pair; 2. neither G, nor Ḡ has a stable cutset; 3. neither G, nor Ḡ has a star-cutset, then G or Ḡ is diamond-free. We show that this conjecture is not valid and that, in a way, every weaker version is false too. To this end, we construct a class of perf...

We consider the Robust Network Loading problem with splittable flows and demands that belong to the budgeted uncertainty set. Four routing schemes are investigated: static, volume, affine and dynamic. First, following what done for static and dynamic routing, we derive capacity formulation for affine and volume routing. This is done using a Benders reformulation approach. Then, we introduce the...