منابع مشابه
Disjoint paths in tournaments
Given k pairs of vertices (si, ti) (1 ≤ i ≤ k) of a digraph G, how can we test whether there exist k vertex-disjoint directed paths from si to ti for 1 ≤ i ≤ k? This is NP-complete in general digraphs, even for k = 2 [2], but for k = 2 there is a polynomial-time algorithm when G is a tournament (or more generally, a semicomplete digraph), due to Bang-Jensen and Thomassen [1]. Here we prove that...
متن کاملDisjoint paths in unions of tournaments
Given k pairs of vertices (si, ti) (1 ≤ i ≤ k) of a digraph G, how can we test whether there exist vertex-disjoint directed paths from si to ti for 1 ≤ i ≤ k? This is NP-complete in general digraphs, even for k = 2 [4], but in [3] we proved that for all fixed k, there is a polynomial-time algorithm to solve the problem if G is a tournament (or more generally, a semicomplete digraph). Here we pr...
متن کاملEdge-disjoint Hamiltonian Paths and Cycles in Tournaments
We describe sufficient conditions for the existence of Hamiltonian paths in oriented graphs and use these to provide a complete description of the tournaments with no two edge-disjoint Hamiltonian paths. We prove that tournaments with small irregularity have many edge-disjoint Hamiltonian cycles in support of Kelly's conjecture.
متن کاملDisjoint Paths in Metacube
A new interconnection network with low-degree for very large parallel computers called metacube (MC) has been introduced recently. The MC network has short diameter similar to that of the hypercube. However, the degree of an MC network is much lower than that of a hypercube of the same size. More than one hundred of millions of nodes can be connected by an MC network with up to 6 links per node...
متن کاملDetermining conditions sufficient for the existence of arc-disjoint hamiltonian paths and out-branchings in tournaments
We study problems closely related to the question raised by Bang-Jensen in [1]: When does a tournament a hamiltonian path and out-branching rooted at the same vertex, arc-disjoint from one another? We answer this question under various circumstances, in some cases managing to show that the out-branching can be taken to be path-like or star-like, and in other cases showing that multiple out-bran...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2015
ISSN: 0001-8708
DOI: 10.1016/j.aim.2014.11.011