Concept

Distance-hereditary graph

Related publications (24)

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Assembling a Network out of Ambiguous Patches

Matthias Grossglauser, Lyudmila Yartseva, Jefferson Elbert Simões

Many graph mining and network analysis problems rely on the availability of the full network over a set of nodes. But inferring a full network is sometimes non-trivial if the raw data is in the form of many small {\em patches} or subgraphs, of the true net ...

2016

Two notions of unit distance graphs

Andrei Kupavskii

A faithful (unit) distance graph in R-d is a graph whose set of vertices is a finite subset of the d-dimensional Euclidean space, where two vertices are adjacent if and only if the Euclidean distance between them is exactly 1. A (unit) distance graph in Rd ...

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

Coloring Triangle-Free Rectangular Frame Intersection Graphs with O(loglogn) Colors

Bartosz Maria Walczak

Recently, Pawlik et al. have shown that triangle-free intersection graphs of line segments in the plane can have arbitrarily large chromatic number. Specifically, they construct triangle-free segment intersection graphs with chromatic number Θ(log log n). ...

2013

Coloring K-k-free intersection graphs of geometric objects in the plane

János Pach

The intersection graph of a collection C of sets is the graph on the vertex set C, in which C-1 . C-2 is an element of C are joined by an edge if and only if C-1 boolean AND C-2 not equal empty set. Erdos conjectured that the chromatic number of triangle-f ...

2012

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 ...

2009

Optimistic chordal coloring: a coalescing heuristic for SSA form programs

Paolo Ienne, Philip Brisk, Ajay Kumar Verma

The interference graph for a procedure in Static Single Assignment (SSA) Form is chordal. Since the k-colorability problem can be solved in polynomial-time for chordal graphs, this result has generated interest in SSA-based heuristics for spilling and coal ...

Springer US2009

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

Partitioning cographs into cliques and stable sets

Dominique de Werra, Tinaz Ekim

We consider the problem of partitioning the node set of a graph into p cliques and k stable sets, namely the (p,k)-coloring problem. Results have been obtained for general graphs \cite{hellcomp}, chordal graphs \cite{hellchordal} and cacti for the case whe ...

2005