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Grad and classes with bounded expansion III. restricted dualities
We study restricted homomorphism dualities in the context of classes with bounded expansion. This presents a generalization of restricted dualities obtained earlier for bounded degree graphs and also
Colorings and Homomorphisms of Minor Closed Classes
We relate acyclic (and star) chromatic number of a graph to the chromatic number of its minors and as a consequence we show that the set of all triangle free planar graphs is homomorphism bounded by
On Triangle Contact Graphs
It is proved that any plane graph may be represented by a triangle contact system, that is a collection of triangular disks which are disjoint except at contact points, each contact point being a
Bipolar orientations Revisited
Abstract Acyclic orientations with exactly one source and one sink — the so-called bipolar orientations-arise in many graph algorithms and specially in graph drawing. The fundamental properties of
Barycentric systems and stretchability
Using a general resolution of barycentric systems we give a generalization of Tutte's theorem on convex drawing of planar graphs. We deduce a characterization of the edge coverings into pairwise
Grad and classes with bounded expansion II. Algorithmic aspects
It is proved that any fixed graph property of type may be decided in linear time for input graphs in a fixed class with bounded expansion, and it is shown that a class of graphs has sublinear separators if it has sub-exponential expansion.
First order properties on nowhere dense structures
It is shown that class with bounded expansion and (newly defined) classes with bounded local expansion and even (very general) nowhere dense classes are quasi wide and that any homomorphism closed first order definable property restricted to a bounded expansion class is a restricted duality.
A left-first search algorithm for planar graphs
We give anO(|V(G)|)-time algorithm to assign vertical and horizontal segments to the vertices of any bipartite plane graphG so that (i) no two segments have an interior point in common, and (ii) two
A Unified Approach to Structural Limits and Limits of Graphs with Bounded Tree-Depth
In this paper we introduce a general framework for the study of limits of relational structures in general and graphs in particular, which is based on a combination of model theory and (functional)
This lecture deals with some consideration on genetic, mechanical aspects concerning the development of folds, noting that stress alone is insufficient to cause folding.