- Tytuł:
- Minimal trees and monophonic convexity
- Autorzy:
-
Cáceres, Jose
Oellermann, Ortrud
Puertas, M. - Powiązania:
- https://bibliotekanauki.pl/articles/743292.pdf
- Data publikacji:
- 2012
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
minimal trees
monophonic intervals of sets
k-monophonic convexity
convex geometries - Opis:
- Let V be a finite set and a collection of subsets of V. Then is an alignment of V if and only if is closed under taking intersections and contains both V and the empty set. If is an alignment of V, then the elements of are called convex sets and the pair (V, ) is called an alignment or a convexity. If S ⊆ V, then the convex hull of S is the smallest convex set that contains S. Suppose X ∈ ℳ. Then x ∈ X is an extreme point for X if X∖{x} ∈ ℳ. A convex geometry on a finite set is an aligned space with the additional property that every convex set is the convex hull of its extreme points. Let G = (V,E) be a connected graph and U a set of vertices of G. A subgraph T of G containing U is a minimal U-tree if T is a tree and if every vertex of V(T)∖U is a cut-vertex of the subgraph induced by V(T). The monophonic interval of U is the collection of all vertices of G that belong to some minimal U-tree. Several graph convexities are defined using minimal U-trees and structural characterizations of graph classes for which the corresponding collection of convex sets is a convex geometry are characterized.
- Źródło:
-
Discussiones Mathematicae Graph Theory; 2012, 32, 4; 685-704
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł