Jaroslav Nesetril

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We introduce classes of graphs with bounded expansion as a generalization of both proper minor closed classes and degree bounded classes. Such classes are based on a new invariant, the greatest reduced average density (grad) of G with rank r, ∇r(G). For these classes we prove the existence of several partition results such as the existence of low tree-width(More)
We provide a correspondence between the subjects of duality and density in classes of finite relational structures. The purpose of duality is to characterise the structures C that do not admit a homomorphism into a given target B by the existence of a homomorphism from a structure A into C. Density is the order-theoretic property of containing no covers (or(More)
Bor uvka presented in 1926 the /rst solution of the Minimum Spanning Tree Problem (MST) which is generally regarded as a cornerstone of Combinatorial Optimization. In this paper we present the /rst English translation of both of his pioneering works. This is followed by the survey of development related to the MST problem and by remarks and historical(More)
Classes of graphs with bounded expansion are a generalization of both proper minor closed classes and degree bounded classes. Such classes are based on a new invariant, the greatest reduced average density (grad) of G with rank r, ∇r(G). These classes are also characterized by the existence of several partition results such as the existence of low(More)