منابع مشابه
Fractional Packing of T-Joins
Given a graph with nonnegative capacities on its edges, it is well known that the capacity of a minimum T -cut is equal to the value of a maximum fractional packing of T -joins. Padberg-Rao’s algorithm finds a minimum capacity T -cut but it does not produce a T -join packing, we present a polynomial combinatorial algorithm for finding an optimal T -join packing.
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 کاملAdvances in packing directed joins
Several of the finest unclaimed prizes in directed graph theory involve the packing of directed joins. One difficulty in claiming these prizes is that the broad conjecture posed by Edmonds and Giles, whether the maximum number of disjoint directed joins equals the smallest weight of a directed cut in every weighted directed graph, is not true in general. This is despite the fact that the conjec...
متن کاملPacking six T-joins in plane graphs
Let G be a plane graph and T an even subset of its vertices. It has been conjectured that if all T -cuts of G have the same parity and the size of every T -cut is at least k, then G contains k edge-disjoint T -joins. The case k = 3 is equivalent to the Four Color Theorem, and the cases k = 4, which was conjectured by Seymour, and k = 5 were proved by Guenin. We settle the next open case k = 6.
متن کاملOn shortest T-joins and packing T-cuts
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...
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ژورنال
عنوان ژورنال: SIAM Journal on Discrete Mathematics
سال: 2004
ISSN: 0895-4801,1095-7146
DOI: 10.1137/s0895480102409619