# Maximum Cycle Packing in Eulerian Graphs Using Local Traces

• Volume: 35, Issue: 1, page 121-132
• ISSN: 2083-5892

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## Abstract

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For a graph G = (V,E) and a vertex v ∈ V , let T(v) be a local trace at v, i.e. T(v) is an Eulerian subgraph of G such that every walk W(v), with start vertex v can be extended to an Eulerian tour in T(v). We prove that every maximum edge-disjoint cycle packing Z* of G induces a maximum trace T(v) at v for every v ∈ V . Moreover, if G is Eulerian then sufficient conditions are given that guarantee that the sets of cycles inducing maximum local traces of G also induce a maximum cycle packing of G.

## How to cite

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Peter Recht, and Eva-Maria Sprengel. "Maximum Cycle Packing in Eulerian Graphs Using Local Traces." Discussiones Mathematicae Graph Theory 35.1 (2015): 121-132. <http://eudml.org/doc/271227>.

@article{PeterRecht2015,
abstract = {For a graph G = (V,E) and a vertex v ∈ V , let T(v) be a local trace at v, i.e. T(v) is an Eulerian subgraph of G such that every walk W(v), with start vertex v can be extended to an Eulerian tour in T(v). We prove that every maximum edge-disjoint cycle packing Z* of G induces a maximum trace T(v) at v for every v ∈ V . Moreover, if G is Eulerian then sufficient conditions are given that guarantee that the sets of cycles inducing maximum local traces of G also induce a maximum cycle packing of G.},
author = {Peter Recht, Eva-Maria Sprengel},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {edge-disjoint cycle packing; local traces; extremal problems in graph theory},
language = {eng},
number = {1},
pages = {121-132},
title = {Maximum Cycle Packing in Eulerian Graphs Using Local Traces},
url = {http://eudml.org/doc/271227},
volume = {35},
year = {2015},
}

TY - JOUR
AU - Peter Recht
AU - Eva-Maria Sprengel
TI - Maximum Cycle Packing in Eulerian Graphs Using Local Traces
JO - Discussiones Mathematicae Graph Theory
PY - 2015
VL - 35
IS - 1
SP - 121
EP - 132
AB - For a graph G = (V,E) and a vertex v ∈ V , let T(v) be a local trace at v, i.e. T(v) is an Eulerian subgraph of G such that every walk W(v), with start vertex v can be extended to an Eulerian tour in T(v). We prove that every maximum edge-disjoint cycle packing Z* of G induces a maximum trace T(v) at v for every v ∈ V . Moreover, if G is Eulerian then sufficient conditions are given that guarantee that the sets of cycles inducing maximum local traces of G also induce a maximum cycle packing of G.
LA - eng
KW - edge-disjoint cycle packing; local traces; extremal problems in graph theory
UR - http://eudml.org/doc/271227
ER -

## References

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