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Monochromatic kernel-perfectness of special classes of digraphs

100%

Galeana-Sánchez H., Ramírez L.

Discussiones Mathematicae Graph Theory

2007

tom 27

nr 3

389-400

In this paper, we introduce the concept of monochromatic kernel-perfect digraph, and we prove the following two results: (1) If D is a digraph without monochromatic directed cycles, then D and each $α_v,v ∈ V(D)$ are monochromatic kernel-perfect digraphs if and only if the composition over D of $(α_v)_{v ∈ V(D)}$ is a monochromatic kernel-perfect digraph. (2) D is a monochromatic kernel-perfect digraph if and only if for any B ⊆ V(D), the duplication of D over B, $D^B$, is a monochromatic kernel-perfect digraph.

Compositions of simple maps

75%

Krzempek J.

Fundamenta Mathematicae

1999

tom 162

nr 2

149-162

A map (= continuous function) is of order ≤ k if each of its point-inverses has at most k elements. Following [4], maps of order ≤ 2 are called simple. Which maps are compositions of simple closed [open, clopen] maps? How many simple maps are really needed to represent a given map? It is proved herein that every closed map of order ≤ k defined on an n-dimensional metric space is a composition of (n+1)k-1 simple closed maps (with metric domains). This theorem fails to be true for non-metrizable spaces. An appropriate map on a Cantor cube of uncountable weight is described.

Ograniczanie wyników

1 Discussiones Mathematicae Graph Theory

1 Fundamenta Mathematicae

1 Galeana-Sánchez H.

1 Krzempek J.

1 Ramírez L.

1 2007

1 1999

Wyniki wyszukiwania

Monochromatic kernel-perfectness of special classes of digraphs

Compositions of simple maps