The depression of a graph and k-kernels

• Autorzy: Mark Schurch , Christine Mynhardt
• Języki publikacji: EN

Abstrakty

EN

An edge ordering of a graph G is an injection f : E(G) → R, the set of real numbers. A path in G for which the edge ordering f increases along its edge sequence is called an f-ascent ; an f-ascent is maximal if it is not contained in a longer f-ascent. The depression of G is the smallest integer k such that any edge ordering f has a maximal f-ascent of length at most k. A k-kernel of a graph G is a set of vertices U ⊆ V (G) such that for any edge ordering f of G there exists a maximal f-ascent of length at most k which neither starts nor ends in U. Identifying a k-kernel of a graph G enables one to construct an infinite family of graphs from G which have depression at most k. We discuss various results related to the concept of k-kernels, including an improved upper bound for the depression of trees.

Słowa kluczowe

EN

edge ordering of a graph; increasing path; monotone path; de- pression

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2014
• Tom: 34
• Numer: 2
• Strony: 233-247

Daty

wydano

2014-05-01

online

2014-04-12

Twórcy

autor

Mark Schurch

• Department of Mathematics and Statistics University of Victoria, P.O. Box 3060 STN CSC Victoria, BC, Canada V8W 3R4

autor

Christine Mynhardt

• Department of Mathematics and Statistics University of Victoria, P.O. Box 3060 STN CSC Victoria, BC, Canada V8W 3R4

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Identyfikatory

DOI

10.7151/dmgt.1736