We continue the study of regular partitions of hypergraphs. In particular, we obtain corresponding counting lemmas for the regularity lemmas for hypergraphs from our paper ‘Regular Partitions of Hypergraphs: Regularity ...

We discuss a game theoretic variant of the subset sum problem, in which two players compete for a common resource represented by a knapsack. Each player owns a private set of items, players pack items alternately, and each ...

Research on the robustness of networks, and in particular the Internet, has gained critical importance in recent decades because more and more individuals, societies and firms rely on this global network infrastructure for ...

We consider a mollifying operator with variable step that, in contrast to the standard mollification, is able to preserve the boundary values of functions. We prove boundedness of the operator in all basic Lebesgue, Sobolev ...

We consider instances of the maximum independent set problem that are constructed according to the following semirandom model. Let $G_{n,p}$ be a random graph, and let $S$ be a set of $k$ vertices, chosen uniformly at ...

Mader asked whether every $C_4$-free graph $G$ contains a subdivision of a complete graph whose order is at least linear in the average degree of $G$. We show that there is a subdivision of a complete graph whose order is ...

We show how to generate labelled and unlabelled outerplanar graphs with $n$ vertices uniformly at random in polynomial time in $n$. To generate labelled outerplanar graphs, we present a counting technique using the ...

We study the Lovász number $\vartheta$ along with two related SDP relaxations $\vartheta_{1/2}$, $\vartheta_2$ of the independence number and the corresponding relaxations $\bar\vartheta$, $\bar\vartheta_{1/2}$, $\bar\vartheta_2$ ...

Complete disorder is impossible – this theme of Ramsey Theory, as stated by Theodore S. Motzkin, was a guiding theme throughout Walter Deuber's scientific life.

In 1978, Dhar suggested a model of a lattice gas whose states are partial orders. In this context he raised the question of determining the number of partial orders with a fixed number of comparable pairs. Dhar conjectured ...