𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Blocking set free configurations and their relations to digraphs and hypergraphs

✍ Scribed by Harald Gropp

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
792 KB
Volume
165-166
Category
Article
ISSN
0012-365X

No coin nor oath required. For personal study only.

✦ Synopsis

The current state of knowledge concerning the existence of blocking set free configurations is given together with a short history of this problem which has also been dealt with in terms of digraphs without even dicycles or 3-chromatic hypergraphs.

The question is extended to the case of nonsymmetric configurations (u,, b3). It is proved that for each value of I > 3 there are only finitely many values of u for which the existence of a blocking set free configuration is still unknown.

πŸ“œ SIMILAR VOLUMES

Rado's selection principle: applications
Rado's selection principle: applications to binary relations, graph and hypergraph colorings and partially ordered sets
✍ Miroslaw Truszczynski; Zsolt Tuza πŸ“‚ Article πŸ“… 1992 πŸ› Elsevier Science 🌐 English βš– 917 KB

Three formulations and various consequences of a compactness principle are given. For example it is shown that an infinite partially ordered set has the jump number at most k if and only if none of its finite subsets has the jump number greater than k. Other applications include Ramsey-type results

Equations in free semigroups with involu
Equations in free semigroups with involution and their relation to equations in free groups
✍ Claudio GutiΓ©rrez πŸ“‚ Article πŸ“… 2003 πŸ› Elsevier Science 🌐 English βš– 130 KB

A free semigroup with involution (FSI) is essentially the set of words over a given alphabet plus an operator which reverses words. The paper introduces equations in FSI and show that they are the right objects to deal with when studying the complexity of equations in free groups. On these lines, we