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Alternating paths in edge-colored complete graphs. (English) Zbl 0819.05039
An alternating path in an edge-colored graph is a path in which every two adjacent edges have different colors. In this paper, an \(O(n^{2.5})\) algorithm is given for finding the maximum number of internally vertex- disjoint alternating paths between a specified pair of vertices in an edge-colored complete graph. Related problems are studied in which further restrictions on the paths and on the edge-colorings are imposed.

MSC:
05C38 Paths and cycles
05C15 Coloring of graphs and hypergraphs
68R10 Graph theory (including graph drawing) in computer science
68Q25 Analysis of algorithms and problem complexity
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[1] Aho, A.; Hopcroft, J.; Ullman, J., Data structures and algorithms, (1983), Addison-Wesley Reading, MA
[2] Alt, H.; Blum, N.; Mehlhorn, K.; Paul, M., Computing a maximum cardinality matching in a bipartite graph in time \( O(n\^{}\{32\}(m/log n)\^{}\{12\})\), Inform. process. lett., 37, 237-240, (1991) · Zbl 0714.68036
[3] Bankfalvi, M.; Bankfalvi, Z., Alternating circuit in two-colored complete graphs, (), 11-18 · Zbl 0159.54202
[4] Benkouar, A.; Manoussakis, Y.; Paschos, V.; Saad, R., On the complexity of Hamiltonian and Eulerian problems in edge-colored complete graphs, (), 190-198 · Zbl 0868.90128
[5] A. Benkouar, Y. Manoussakis and R. Saad, Alternating cycles through fixed vertices in edge-colored graphs, J. Combin. Math. Combin. Comput., to appear. · Zbl 0813.05042
[6] A. Benkouar, Y. Manoussakis and R. Saad, Edge-colored complete graphs containing alternating hamiltonian cycles, submitted. · Zbl 1017.05068
[7] Bollodas, R.; Erdös, P., Alternating Hamiltonian cycles, Israel J. math., 23, 126-130, (1976)
[8] Chen, C.C.; Daykin, D.E., Graph with Hamiltonian cycles having adjacent lines different colors, J. combin. theory ser. B, 21, 135-139, (1976) · Zbl 0287.05106
[9] Dijkstra, E.W., A note on two problems in connexion with graphs, Numer. math., 1, 269-271, (1959) · Zbl 0092.16002
[10] Even, S.; Kariv, O., An O(n2.5) algorithm for maximum matchings in general graphs, (), 100-112
[11] Fortune, S.; Hopcroft, J.; Wyllie, J., The directed subgraph homeomorphism problem, Theoret. comput. sci., 10, 111-121, (1980) · Zbl 0419.05028
[12] Garey, M.; Johnson, D., Computers and intractability — A guide to the theory of NP-complete-Ness, (1979), Freeman New York
[13] Hell, P.; Manoussakis, Y.; Tuza, Zs., Packing problems in edge-colored graphs, Discrete appl. math., 52, 295-306, (1994) · Zbl 0806.05054
[14] Lovasz, L.; Plummer, M., Matching theory, () · Zbl 0618.05001
[15] N. Robertson and P.D. Seymour, On graph minors XIII, The disjoint path problem, to appear. · Zbl 0823.05038
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