Publications related to On some coloring problems in grids

Triangle-Free Geometric Intersection Graphs with Large Chromatic Number

Several classical constructions illustrate the fact that the chromatic number of a graph may be arbitrarily large compared to its clique number. However, until very recently no such construction was known for intersection graphs of geometric objects in the ...

Springer US2013

On coloring problems with local constraints

Yuri Faenza

We deal with some generalizations of the graph coloring problem on classes of perfect graphs. Namely we consider the μ-coloring problem (upper bounds for the color on each vertex), the precoloring extension problem (a subset of vertices colored beforehand) ...

Elsevier2012

A note on chromatic properties of threshold graphs

Dominique de Werra, Bernard Ries, Rico Zenklusen

In threshold graphs one may find weights for the vertices and a threshold value t such that for any subset S of vertices, the sum of the weights is at most the threshold t if and only if the set S is a stable (independent) set. In this note we ask a simila ...

2012

Coloring fuzzy circular interval graphs

Friedrich Eisenbrand, Martin Niemeier

Given a graph G with nonnegative node labels w, a multiset of stable sets S_1,...,S_k\subseteq V(G) such that each vertex v \in V(G) is contained in w(v) many of these stable sets is called a weighted coloring. The weighted coloring number \chi_w(G) is the ...

Elsevier2012

Universal Sets for Straight-Line Embeddings of Bicolored Graphs

Jan Kyncl

A set S of n points is 2-color universal for a graph G on n vertices if for every proper 2-coloring of G and for every 2-coloring of S with the same sizes of color classes as G has, G is straight-line embeddable on S. We show that the so-called double chai ...

2011

Complexity of the critical node problem over trees

Marco Di Summa

In this paper we deal with the critical node problem (CNP), i.e., the problem of searching for a given number K of nodes in a graph G, whose removal minimizes the (weighted or unweighted) number of connections between pairs of nodes in the residual graph. ...

2011

The potential to improve the choice: list conflict-free coloring for geometric hypergraphs

Shakhar Smorodinsky

Given a geometric hypergraph (or a range-space)

H=(V,\cal E)

, a coloring of its vertices is said to be conflict-free if for every hyperedge

S \in \cal E

there is at least one vertex in

S

whose color is distinct from the colors of all other vertices i ...

2010

Blockers and transversals in some subclasses of bipartite graphs: When caterpillars are dancing on a grid

Dominique de Werra, Bernard Ries

Given an undirected graph G = (V, E) with matching number nu(G), a d-blocker is a subset of edges B such that nu((V, E \ B))

2010

An Optimal Linear-Time Algorithm for Interprocedural Register Allocation in High Level Synthesis Using SSA Form

Paolo Ienne, Philip Brisk, Ajay Kumar Verma

An optimal linear-time algorithm for interprocedural register allocation in high level synthesis is presented. Historically, register allocation has been modeled as a graph coloring problem, which is nondeterministic polynomial time-complete in general; ho ...

2010

Coloring axis-parallel rectangles

János Pach, Gábor Tardos

For every k and r, we construct a finite family of axis-parallel rectangles in the plane such that no matter how we color them with k colors, there exists a point covered by precisely r members of the family, all of which have the same color. For r = 2, th ...

2010

On some coloring problems in grids

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Triangle-Free Geometric Intersection Graphs with Large Chromatic Number

On coloring problems with local constraints

A note on chromatic properties of threshold graphs

Coloring fuzzy circular interval graphs

Universal Sets for Straight-Line Embeddings of Bicolored Graphs

Complexity of the critical node problem over trees

The potential to improve the choice: list conflict-free coloring for geometric hypergraphs

Blockers and transversals in some subclasses of bipartite graphs: When caterpillars are dancing on a grid

An Optimal Linear-Time Algorithm for Interprocedural Register Allocation in High Level Synthesis Using SSA Form

Coloring axis-parallel rectangles

Complexity of the critical node problem over trees

Blockers and transversals in some subclasses of bipartite graphs: When caterpillars are dancing on a grid

Coloring axis-parallel rectangles

The potential to improve the choice: list conflict-free coloring for geometric hypergraphs

Coloring fuzzy circular interval graphs

On coloring problems with local constraints

Universal Sets for Straight-Line Embeddings of Bicolored Graphs

An Optimal Linear-Time Algorithm for Interprocedural Register Allocation in High Level Synthesis Using SSA Form

Triangle-Free Geometric Intersection Graphs with Large Chromatic Number

A note on chromatic properties of threshold graphs