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- István Miklós, Péter L. Erdös, Lajos Soukup
- Electr. J. Comb.
- 2013

In this paper we consider a simple Markov chain for bipartite graphs with given degree sequence on n vertices. We show that the mixing time of this Markov chain is bounded above by a polynomial in n… (More)

Continuing [6], [8] and [15], we study the consequences of the weak Freese-Nation property of (P(ω),⊆). Under this assumption, we prove that most of the known cardinal invariants including all of… (More)

Let X be a set, κ be a cardinal number and let H be a family of subsets of X which covers each x ∈ X at least κ times. What assumptions can ensure that H can be decomposed into κ many disjoint… (More)

We introduce a general method of constructing locally compact scattered spaces from certain families of sets and then, with the help of this method, we prove that if κ = κ then there is such a space… (More)

Denote by G and D, respectively, the the homomorphism poset of the finite undirected and directed graphs, respectively. A maximal antichain A in a poset P splits if A has a partition (B, C) such that… (More)

- Lajos Soukup
- Discrete Mathematics
- 2011

We show that usage of elementary submodels is a simple but powerful method to prove theorems, or to simplify proofs in infinite combinatorics. First we introduce all the necessary concepts of logic,… (More)

- Péter L. Erdös, Lajos Soukup
- Order
- 2010

D denotes the homomorphism poset of finite directed graphs. An antichain duality is a pair 〈F ,D〉 of antichains of D such that (F→) ∪ (→D) = D is a partition. A generalized duality pair in D is an… (More)

- Lajos Soukup
- 2010

The additivity spectrum ADD(I) of an ideal I ⊂ P(I) is the set of all regular cardinals κ such that there is an increasing chain {Aα : α < κ} ⊂ I with ∪α<κAα / ∈ I. We investigate which set A of… (More)

- Sakaé Fuchino, Saharon Shelah, Lajos Soukup
- Ann. Pure Appl. Logic
- 1997

We study combinatorial principles known as stick and club. Several variants of these principles and cardinal invariants connected to them are also considered. We introduce a new kind of side-by-side… (More)

- Péter L. Erdős, Sándor Z. Kiss, István Miklós, Lajos Soukup, Arndt von Haeseler
- PloS one
- 2015

In 1999 Kannan, Tetali and Vempala proposed a MCMC method to uniformly sample all possible realizations of a given graphical degree sequence and conjectured its rapidly mixing nature. Recently their… (More)