Proceedings of the 12th European Conference on Combinatorics, Graph Theory and Applications
We give an infinitary extension of the Ne\v set\v ril--R\"odl theorem for category of relati... more We give an infinitary extension of the Ne\v set\v ril--R\"odl theorem for category of relational structures with special type-respecting embeddings.
The notion of bounded expansion captures uniform sparsity of graph classes and renders various al... more The notion of bounded expansion captures uniform sparsity of graph classes and renders various algorithmic problems that are hard in general tractable. In particular, the model-checking problem for first-order logic is fixed-parameter tractable over such graph classes. With the aim of generalizing such results to dense graphs, we introduce classes of graphs with structurally bounded expansion , defined as first-order transductions of classes of bounded expansion. As a first step towards their algorithmic treatment, we provide their characterization analogous to the characterization of classes of bounded expansion via low treedepth covers (or colorings), replacing treedepth by its dense analogue called shrubdepth.
Proceedings of the 12th European Conference on Combinatorics, Graph Theory and Applications
We give an infinitary extension of the Ne\v set\v ril--R\"odl theorem for category of relati... more We give an infinitary extension of the Ne\v set\v ril--R\"odl theorem for category of relational structures with special type-respecting embeddings.
The notion of bounded expansion captures uniform sparsity of graph classes and renders various al... more The notion of bounded expansion captures uniform sparsity of graph classes and renders various algorithmic problems that are hard in general tractable. In particular, the model-checking problem for first-order logic is fixed-parameter tractable over such graph classes. With the aim of generalizing such results to dense graphs, we introduce classes of graphs with structurally bounded expansion , defined as first-order transductions of classes of bounded expansion. As a first step towards their algorithmic treatment, we provide their characterization analogous to the characterization of classes of bounded expansion via low treedepth covers (or colorings), replacing treedepth by its dense analogue called shrubdepth.
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Papers by Jaroslav Nešetřil