منابع مشابه
Packing 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 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 کاملFractional 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 کامل$T$-Joins in Infinite Graphs
We characterize the class of infinite connected graphs G for which there exists a T -join for any choice of an infinite T ⊆ V (G). We also show that the following well-known fact remains true in the infinite case. If G is connected and does not contain a T -join, then it will if we either remove an arbitrary vertex from T or add any new vertex to T .
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: Journal of Combinatorial Theory, Series B
سال: 2016
ISSN: 0095-8956
DOI: 10.1016/j.jctb.2015.09.002