Temat: weak variety - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: Equational bases for weak monounary varieties
Autorzy:: Bińczak, Grzegorz
Powiązania:: https://bibliotekanauki.pl/articles/729027.pdf
Data publikacji:: 2002
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: partial algebra
weak equation
weak variety
regular equation
regular weak equational theory
monounary algebras
Opis:: It is well-known that every monounary variety of total algebras has one-element equational basis (see [5]). In my paper I prove that every monounary weak variety has at most 3-element equational basis. I give an example of monounary weak variety having 3-element equational basis, which has no 2-element equational basis.
Źródło:: Discussiones Mathematicae - General Algebra and Applications; 2002, 22, 1; 87-100
1509-9415
Pojawia się w:: Discussiones Mathematicae - General Algebra and Applications
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 2.

Tytuł:: On dually compact closed classes of graphs and BFS-constructible graphs
Autorzy:: Polat, Norbert
Powiązania:: https://bibliotekanauki.pl/articles/743184.pdf
Data publikacji:: 2003
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: infinite graph
dismantlable graph
constructible graph
BFS-cons-tructible graph
variety
weak-retract
strong product
bridged graph
Helly graph
weakly-modular graph
dually compact closed class
Opis:: A class C of graphs is said to be dually compact closed if, for every infinite G ∈ C, each finite subgraph of G is contained in a finite induced subgraph of G which belongs to C. The class of trees and more generally the one of chordal graphs are dually compact closed. One of the main part of this paper is to settle a question of Hahn, Sands, Sauer and Woodrow by showing that the class of bridged graphs is dually compact closed. To prove this result we use the concept of constructible graph. A (finite or infinite) graph G is constructible if there exists a well-ordering ≤ (called constructing ordering) of its vertices such that, for every vertex x which is not the smallest element, there is a vertex y < x which is adjacent to x and to every neighbor z of x with z < x. Finite graphs are constructible if and only if they are dismantlable. The case is different, however, with infinite graphs. A graph G for which every breadth-first search of G produces a particular constructing ordering of its vertices is called a BFS-constructible graph. We show that the class of BFS-constructible graphs is a variety (i.e., it is closed under weak retracts and strong products), that it is a subclass of the class of weakly modular graphs, and that it contains the class of bridged graphs and that of Helly graphs (bridged graphs being very special instances of BFS-constructible graphs). Finally we show that the class of interval-finite pseudo-median graphs (and thus the one of median graphs) and the class of Helly graphs are dually compact closed, and that moreover every finite subgraph of an interval-finite pseudo-median graph (resp. a Helly graph) G is contained in a finite isometric pseudo-median (resp. Helly) subgraph of G. We also give two sufficient conditions so that a bridged graph has a similar property.
Źródło:: Discussiones Mathematicae Graph Theory; 2003, 23, 2; 365-381
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

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