منابع مشابه
On Packing T-Cuts
A short proof of a difficult theorem of P.D. Seymour on grafts with the max-flow min-cut property is given.
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Let G be an undirected connected graph. For each u E V(G), the node set of G, and each Fc E(G), the edge set of G, we define dF(u) to be the number of edges in F incident with u. If T& V(G), then we call a set Fs E(G) a T-join if T= {UE V(G)(d,( ) o is odd}. Throughout this paper we shall always assume ( T ( to be even. We denote the minimum cardinality of a T-join in G by z,(G). For UG V(G) we...
متن کاملOn the integral 4-packing of T-cuts
Let C = (V, E) be an undirected graph, w : E + Z’ a weight function and T c V an even subset of vertices from G. A T-cut is an edge-cut set which divides T into two odd sets. For ( Tj = 4 Seymour gave a good characterization of the graphs for which there exists a maximum packing of T-cuts that is integral. Based on Seymour’s characterization we provide a simple 0(n3m + PI”&) algorithm for incre...
متن کاملOn Packing T-Joins
A graft is a graph G = (V,E) together with a set T ⊆ V of even cardinality. A T-cut of G is an edge cut δ(X) for which |X ∩T | is odd. A T-join of G is a set of edges S ⊆ E with the property that a vertex of the graph (V, S) has odd degree if and only if it is in T . A T-join packing of G is a set of pairwise disjoint T-joins. Let τ(G) be the size of the smallest T-cut of G and let ν(G) be the ...
متن کاملPacking disjoint cycles over vertex cuts
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, V1, and V2 such that there is no edge between V1 and V2, and k = |S|, then our results imply that ...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 1994
ISSN: 0095-8956
DOI: 10.1006/jctb.1994.1049