A digraph D = (V, A) is arc-traceable if for each arc xy in A, xy lies on a directed path containing all the vertices of V , i.e. a hamiltonian path. Given a tournament T , it is well known that it contains a directed hamiltonian path. In this paper, we develop the structure necessary for a tournament T to contain an arc xy that is not on any hamiltonian path. Using this structure, we give suff...

Two new algorithms, SPMF and SPMF, for finding the complete chain of solutions of the selection model are presented in this paper. A special kind of residual path, called a λ-directed simple residual path, is identified to be the only kind of residual path necessary for SPMF. By augmenting the right amount of flows along the λ-directed simple residual paths, the new algorithms are monotone conv...

RMIT University Melbourne, BOX 2476V, VIC 3001, Australia, fkist,[email protected] Abstract This paper considers a directed graph G(N;A) with n nodes, m directed arcs and a cost value for each arc. The synthesis of a partially link disjoint pair of paths for a given OD-pair with the minimum total cost is investigated. An algorithm is presented that solves the all-best partially disjoint...

A digraph D = (V, A) is arc-traceable if for each arc xy in A, xy lies on a directed path containing all the vertices of V , i.e., hamiltonian path. We prove a conjecture of Quintas [7]: if D is arc-traceable, then the condensation of D is a directed path. We show that the converse of this conjecture is false by providing an example of an upset tournament which is not arc-traceable. We then giv...