Geodesic
Maximum Cycle Packing in Eulerian Graphs Using Local Traces
Discussiones Mathematicae. Graph Theory, Tome 35 (2015) no. 1, pp. 121-132

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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.
Keywords: edge-disjoint cycle packing, local traces, extremal problems in graph theory 
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Recht, Peter; Sprengel, Eva-Maria. Maximum Cycle Packing in Eulerian Graphs Using Local Traces. Discussiones Mathematicae. Graph Theory, Tome 35 (2015) no. 1, pp. 121-132. http://geodesic.mathdoc.fr/item/DMGT_2015_35_1_a9/