# Sulamita Klein

• SIAM J. Discrete Math.
• 2003
List partitions generalize list colourings and list homomorphisms. Each symmetric matrix M over 0; 1; deenes a list partition problem. Diierent choices of the matrix M lead to many well-known graph the-oretic problems including the problem of recognizing split graphs and their generalizations, nding homogeneous sets, joins, clique cutsets, stable cutsets,(More)
• STOC
• 1999
We introduce a parametrized family of graph problems that includes several well-known graph partition problems as special czses. We develop tools which allow us to classify the complexity of many problems in this family, and in particular lead us to a complete classification for small values of the parameters. Along the way, we obtain a variety of specific(More)
• J. Algorithms
• 2000
A skew partition as defined by Chvátal is a partition of the vertex set of a graph into four nonempty parts A B C D such that there are all possible edges between A and B and no edges between C and D. We present a polynomial-time algorithm for testing whether a graph admits a skew partition. Our algorithm solves the more general list skew partition problem,(More)
• Theor. Comput. Sci.
• 2005
It is well known that a clique with k + 1 vertices is the only minimal obstruction to k-colourability of chordal graphs. A similar result is known for the existence of a cover by cliques. Both of these problems are in fact partition problems, restricted to chordal graphs. The first seeks partitions into k independent sets, and the second is equivalent to(More)
• Inf. Process. Lett.
• 1998
A homogeneous set is a non-trivial module of a graph, i.e. a nonempty, non-unitary, proper subset of a graph’s vertices such that all its elements present exactly the same outer neighborhood. Given two graphs G1(V, E1), G2(V, E2), the Homogeneous Set Sandwich Problem (HSSP) asks whether there exists a sandwich graph GS(V, ES), E1 ⊆ ES ⊆ E2, which has a(More)
• Annals OR
• 2005
In Hell et al. (2004), we have previously observed that, in a chordal graph G, the maximum number of independent r -cliques (i.e., of vertex disjoint subgraphs of G, each isomorphic to Kr , with no edges joining any two of the subgraphs) equals the minimum number of cliques of G that meet all the r -cliques of G. When r = 1, this says that chordal graphs(More)