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For a graph G, let ν(G) and ν (G) denote the maximum cardinalities of packings of vertex-disjoint and edge-disjoint cycles of G, respectively. We study the interplay of these two parameters and vertex cuts in graphs. If G is a graph whose vertex set can be partitioned into three non-empty sets S, V 1 , and V 2 such that there is no edge between V 1 and V 2… (More)

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… (More)

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