
PTAS for Sparse GeneralValued CSPs
We study polynomialtime approximation schemes (PTASes) for constraint s...
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Approximation metatheorem for fractionally treewidthfragile graphs
Baker's technique is a powerful tool for designing polynomialtime appro...
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Clustered Variants of Hajós' Conjecture
Hajós conjectured that every graph containing no subdivision of the comp...
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Injective Objects and Fibered Codensity Liftings
Functor lifting along a fibration is used for several different purposes...
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Sketched Representations and Orthogonal Planarity of Bounded Treewidth Graphs
Given a planar graph G and an integer b, OrthogonalPlanarity is the prob...
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Rankwidth meets stability
We study two notions of being wellstructured for classes of graphs that...
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VC density of set systems defnable in treelike graphs
We study set systems definable in graphs using variants of logic with di...
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TreewidthPliability and PTAS for MaxCSPs
We identify a sufficient condition, treewidthpliability, that gives a polynomialtime approximation scheme (PTAS) for a large class of Max2CSPs parametrised by the class of allowed constraint graphs (with arbitrary constraints on an unbounded alphabet). Our result applies more generally to the maximum homomorphism problem between two rationalvalued structures. The condition unifies the two main approaches for designing PTASes. One is Baker's layering technique, which applies to sparse graphs such as planar or excludedminor graphs. The other is based on Szemerédi's regularity lemma and applies to dense graphs. Albeit with some limitations, we extend the applicability of both techniques to new classes of MaxCSPs. Treewidthpliability turns out to be a robust notion that can be defined in several equivalent ways, including characterisations via size, treedepth, or the Hadwiger number. We show connections to the notions of fractionaltreewidthfragility from structural graph theory, hyperfiniteness from the area of property testing, and regularity partitions from the theory of dense graph limits. These may be of independent interest. In particular we show that a monotone class of graphs is hyperfinite if and only if it is fractionallytreewidthfragile and has bounded degree.
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