| author: | Tomáš Kaiser and Riste Škrekovski |
|---|---|
| title: | Cycles intersecting edge-cuts of prescribed sizes |
| keywords: | graph, cycle, edge-cut, covering cycle, coverable set |
| abstract: |
We prove that every cubic bridgeless graph
G
contains a
2
-factor which intersects all (minimal) edge-cuts of
size
3
or
4
. This generalizes an earlier result of the authors,
namely that such a
2
-factor exists provided that
G
is planar. As a further extension, we show that every
graph contains a cycle (a union of edge-disjoint circuits)
that intersects all edge-cuts of size
3
or
4
. Motivated by this result, we introduce the concept
of a coverable set of integers and discuss a number of
questions, some of which are related to classical problems
of graph theory such as Tutte's
4
-flow conjecture or the Dominating circuit
conjecture.
|
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| reference: | Tomáš Kaiser and Riste Škrekovski (2005), Cycles intersecting edge-cuts of prescribed sizes, in 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), Stefan Felsner (ed.), Discrete Mathematics and Theoretical Computer Science Proceedings AE, pp. 303-308 |
| bibtex: | For a corresponding BibTeX entry, please consider our BibTeX-file. |
| ps.gz-source: | dmAE0160.ps.gz (49 K) |
| ps-source: | dmAE0160.ps (118 K) |
| pdf-source: | dmAE0160.pdf (140 K) |
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