3 research outputs found
Precedence thinness in graphs
Interval and proper interval graphs are very well-known graph classes, for
which there is a wide literature. As a consequence, some generalizations of
interval graphs have been proposed, in which graphs in general are expressed in
terms of interval graphs, by splitting the graph in some special way.
As a recent example of such an approach, the classes of -thin and proper
-thin graphs have been introduced generalizing interval and proper interval
graphs, respectively. The complexity of the recognition of each of these
classes is still open, even for fixed .
In this work, we introduce a subclass of -thin graphs (resp. proper
-thin graphs), called precedence -thin graphs (resp. precedence proper
-thin graphs). Concerning partitioned precedence -thin graphs, we present
a polynomial time recognition algorithm based on -trees. With respect to
partitioned precedence proper -thin graphs, we prove that the related
recognition problem is \NP-complete for an arbitrary and polynomial-time
solvable when is fixed. Moreover, we present a characterization for these
classes based on threshold graphs.Comment: 33 page
Thinness of product graphs
The thinness of a graph is a width parameter that generalizes some properties
of interval graphs, which are exactly the graphs of thinness one. Many
NP-complete problems can be solved in polynomial time for graphs with bounded
thinness, given a suitable representation of the graph. In this paper we study
the thinness and its variations of graph products. We show that the thinness
behaves "well" in general for products, in the sense that for most of the graph
products defined in the literature, the thinness of the product of two graphs
is bounded by a function (typically product or sum) of their thinness, or of
the thinness of one of them and the size of the other. We also show for some
cases the non-existence of such a function.Comment: 45 page
Precedence thinness in graphs
Interval and proper interval graphs are very well-known graph classes, for which there is a wide literature. As a consequence, some generalizations of interval graphs have been proposed, in which graphs in general are expressed in terms of k interval graphs, by splitting the graph in some special way. As a recent example of such an approach, the classes of k-thin and proper k-thin graphs have been introduced generalizing interval and proper interval graphs, respectively. The complexity of the recognition of each of these classes is still open, even for fixed k≥2. In this work, we introduce a subclass of k-thin graphs (resp. proper k-thin graphs), called precedence k-thin graphs (resp. precedence proper k-thin graphs). Concerning partitioned precedence k-thin graphs, we present a polynomial time recognition algorithm based on PQ trees. With respect to partitioned precedence proper k-thin graphs, we prove that the related recognition problem is NP-complete for an arbitrary k and polynomial-time solvable when k is fixed. Moreover, we present a characterization for these classes based on threshold graphs.Fil: Bonomo, Flavia. Consejo Nacional de Investigaciones CientÃficas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigación en Ciencias de la Computación. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigación en Ciencias de la Computación; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; ArgentinaFil: de Souza Oliveira, Fabiano. Universidade do Estado de Rio do Janeiro; BrasilFil: Sampaio Jr., Moysés S.. Universidade Federal do Rio de Janeiro; BrasilFil: Szwarcfiter, Jayme L.. Universidade Federal do Rio de Janeiro; Brasil. Universidade do Estado de Rio do Janeiro; Brasi