On Symmetric and Antisymmetric Relations.
Historická perspektiva konečné matematiky
Kombinatorické konstrukce, jejich složitost a praktický význam
O studentském semináři z teorie grafů na Matematicko-fyzikální fakultě KU
-хроматические графы вез циклов длины
László Lovász a jeho matematika (Abelova cena za rok 2021)
Tento článek je napsán u příležitosti udělení Abelovy ceny za rok 2021 László Lovászovi.
On uniquely colorable graphs without short cycles
Combinatorics and quantifiers
Let be the set of subsets of of cardinality . Let be a coloring of and a coloring of . We write if every -homogeneous is also -homogeneous. The least such that for some is called the of and denoted by . In the first part of the paper we prove the existence of colorings with high -width. In particular, we show that for each and there is a coloring with . In the second part of the paper we give applications of wide colorings in the theory of generalized quantifiers....
Riga -point
On reconstructing of infinite forests
Every group is a maximal subgroup of the semigroup of relations
Graphs with small asymmetries
A few remarks on the history of MST-problem
On the background of Borůvka’s pioneering work we present a survey of the development related to the Minimum Spanning Tree Problem. We also complement the historical paper Graham-Hell [GH] by a few remarks and provide an update of the extensive literature devoted to this problem.
Infinite precise objects
On maximal finite antichains in the homomorphism order of directed graphs
We show that the pairs where T is a tree and its dual are the only maximal antichains of size 2 in the category of directed graphs endowed with its natural homomorphism ordering.
Práce Vojtěcha Jarníka v kombinatorické optimalizaci
The Erdős-Turán property for a class of bases
Universality of directed graphs of a given height
More on the complexity of cover graphs
In response to [3] and [4] we prove that the recognition of cover graphs of finite posets is an NP-hard problem.
Linear programming duality and morphisms
In this paper we investigate a class of problems permitting a good characterisation from the point of view of morphisms of oriented matroids. We prove several morphism-duality theorems for oriented matroids. These generalize LP-duality (in form of Farkas' Lemma) and Minty's Painting Lemma. Moreover, we characterize all morphism duality theorems, thus proving the essential unicity of Farkas' Lemma. This research helped to isolate perhaps the most natural definition of strong maps for oriented matroids....
Page 1 Next