Two are disjoint paths in Eulerian digraphs
- Kyoto Univ. (Japan)
Let G be an Eulerian digraph, and x{sub 1}, x{sub 2}, y{sub 1}, y{sub 2} be four vertices (called terminals) in G. A polynomial time algorithm is presented to decide whether G contains two arc-disjoint x{sub i}x{sub j}- and y{sub k}y{sub l}- paths, where i, j = k, l = 1, 2 (i.e., directions of these directed paths can be chosen arbitrarily). The algorithm is based on the following characterization of minimal infeasible instances of the problem. An instance is minimal infeasible (i.e., any instance obtained by contracting an arc becomes feasible) if and only if it satisfies the following conditions. (i) G is planar, and has at most one cut vertex. (ii) All the terminals have degree 2, and all other vertices have degree 4. (iii) G has a planar representation in which every face is a directed cycle (or equivalently, the arcs indident to a vertex are alternatively oriented out and in), and all the terminals lie on the boundary of one common face in the order of x{sub 1}, y{prime}, x{sub 2}, y{double_prime}, where (y{prime}, y{double_prime}) = (y{sub 1}, y{sub 2}). This is an extension of the previously known characterization of weak 3-linkings (i.e., the case of three terminals, in which the directions of three arc disjoint paths are prespecified). if G is a general digraph, it is easily shown that the problem is NP-complete.
- OSTI ID:
- 36148
- Report Number(s):
- CONF-9408161--
- Country of Publication:
- United States
- Language:
- English
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