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• # Artykuł - szczegóły

## Discussiones Mathematicae Graph Theory

2014 | 34 | 2 | 233-247

## The depression of a graph and k-kernels

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.

EN

233-247

wydano
2014-05-01
online
2014-04-12

### Twórcy

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

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