منابع مشابه
Disjoint dijoins
A “dijoin” in a digraph is a set of edges meeting every directed cut. D. R. Woodall conjectured in 1976 that if G is a digraph, and every directed cut of G has at least k edges, then there are k pairwise disjoint dijoins. This remains open, but a capacitated version is known to be false. In particular, A. Schrijver gave a digraph G and a subset S of its edge-set, such that every directed cut co...
متن کاملA note on disjoint dijoins
If q is a prime power, D is a directed graph such that the underlying undirected graph is (q−1, 1)-partition-connected, then D contains q disjoint dijoins.
متن کاملA Note on Dijoins
For every nonnegative integer arc weight function w, the minimum weight of a dicut is at least as large as the maximum number of dijoins such that no arc a is contained in more than w(a) of these dijoins. We give two examples of digraphs with strict inequality for some weight w and discuss the possibility that, together with an example due to Schrijver, these are the only “minimal” such examples.
متن کاملVisualizing, Finding and Packing Dijoins
We consider the problem of making a directed graph strongly connected. To achieve this, we are allowed for assorted costs to add the reverse of any arc. A successful set of arcs, called a dijoin, must intersect every directed cut. Lucchesi and Younger gave a min-max theorem for the problem of finding a minimum cost dijoin. Less understood is the extent to which dijoins pack. One difficulty is t...
متن کاملDisjoint Polymorphism
The combination of intersection types, a merge operator and parametric polymorphism enables important applications for programming. However, such combination makes it hard to achieve the desirable property of a coherent semantics: all valid reductions for the same expression should have the same value. Recent work proposed disjoint intersections types as a means to ensure coherence in a simply ...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 2016
ISSN: 0095-8956
DOI: 10.1016/j.jctb.2016.04.002