Concept

Perfect graph theorem

Publications associées (21)

Detecting nanoscale vibrations as signature of life

Giovanni Dietler, Sandor Kasas, Giovanni Longo, Francesco Simone Ruggeri, Petar Stupar

The existence of life in extreme conditions, in particular in extraterrestrial environments, is certainly one of the most intriguing scientific questions of our time. In this report, we demonstrate the use of an innovative nanoscale motion sensor in life-s ...

National Academy of Sciences2015

An extremal problem on crossing vectors

Bartosz Maria Walczak, Michal Lason

For positive integers w and k, two vectors A and B from Z(w) are called k-crossing if there are two coordinates i and j such that A[i] - B[i] >= k and B[j] - A[j] >= k. What is the maximum size of a family of pairwise 1-crossing and pairwise non-k-crossing ...

Academic Press Inc Elsevier Science2014

Triangle-free intersection graphs of line segments with large chromatic number

Bartosz Maria Walczak, Michal Lason

In the 1970s Erdos asked whether the chromatic number of intersection graphs of line segments in the plane is bounded by a function of their clique number. We show the answer is no. Specifically, for each positive integer k we construct a triangle-free fam ...

Academic Press Inc Elsevier Science2014

Graph Transformations preserving the stability number

Dominique de Werra

We analyze the relations between several graph transformations that were introduced to be used in procedures determining the stability number of a graph. We show that all these transformations can be decomposed into a sequence of edge deletions and twin de ...

Elsevier Science Bv2012

Graph transformations preserving the stability number

Dominique de Werra

We analyse the relations between several graph transformations that were introduced to be used in procedures determining the stability number of a graph. We show that all these transformations can be decomposed into a sequence of edge deletions and twin de ...

2009

Characterizing Path Graphs by Forbidden Induced Subgraphs

A path graph is the intersection graph of subpaths of a tree. In 1970, Renz asked for a characterization of path graphs by forbidden induced subgraphs. We answer this question by determining the complete list of graphs that are not path graphs and are mini ...

2009

On the inapproximability of independent domination in 2P3-free perfect graphs

Dominique de Werra

We consider the complexity of approximation for the INDEPENDENT DOMINATING SET problem in 2P(3)-free graphs, i.e., graphs that do not contain two disjoint copies of the chordless path on three vertices as all induced subgraph. We show that, if P not equal ...

2009

Partitioning graphs into complete and empty graphs

Tinaz Ekim

Given integers j and k and a graph G, we consider partitions of the vertex set of G into j + k parts where j of these parts induce empty graphs and the remaining k induce cliques. If such a partition exists, we say G is a (j, k)-graph. For a fixed j and k ...

Elsevier2009

Polarity of chordal graphs

Dominique de Werra, Tinaz Ekim

Polar graphs are a common generalization of bipartite, cobipartite, and split graphs. They are defined by the existence of a certain partition of vertices, which is NP-complete to decide for general graphs. It has been recently proved that for cographs, th ...

2008

Polar cographs

Dominique de Werra, Tinaz Ekim

Polar graphs are a natural extension of some classes of graphs like bipartite graphs, split graphs and complements of bipartite graphs. A graph is (s, k)-polar if there exists a partition A, B of its vertex set such that A induces a complete s-partite grap ...

Elsevier2008