Packing arc-disjoint cycles in oriented graphs
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Packing Arc-Disjoint Cycles in Tournaments
AbstractA tournament is a directed graph in which there is a single arc between every pair of distinct vertices. Given a tournament T on n vertices, we explore the classical and parameterized complexity of the problems of determining if T has a cycle ...
Disjoint Cycles in Eulerian Digraphs and the Diameter of Interchange Graphs
Let R=(r1, , rm) and S=(s1, , sn) be nonnegative integral vectors with ri= sj. Let A(R, S) denote the set of all m n {0, 1}-matrices with row sum vector R and column sum vector S. Suppose A(R, S) . The interchange graphG(R, S) of A(R, S) was defined by ...
Arc-Disjoint Cycles and Feedback Arc Sets
Isaak posed the following problem. Suppose T is a tournament having a minimum feedback arc set, which induces an acyclic digraph with a hamiltonian path. Is it true that the maximum number of arc-disjoint cycles in T equals the cardinality of minimum ...
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