zbMATH — the first resource for mathematics

Highly connected non-2-linked digraphs. (English) Zbl 0746.05030
A digraph \(D\) is said to be 2-linked if for any four vertices \(x_ 1\), \(x_ 2\), \(y_ 1\), and \(y_ 2\) there exist disjoint directed paths \(P_ 1\) and \(P_ 2\) starting at \(x_ 1\) and \(x_ 2\) and ending at \(y_ 1\) and \(y_ 2\), respectively. The author shows that for every positive integers \(k\) there exists a strongly \(k\)-connected digraph \(D\) that is not 2-linked.

05C20 Directed graphs (digraphs), tournaments
05C38 Paths and cycles
05C40 Connectivity
Full Text: DOI
[1] J. C. Bermond, andL. Lovász: Problem 3, in:Recent advances in graph theory, Proc. Coll. Prague, Academic Prague (1975), 541.
[2] J. C. Bermond, andC. Thomassen: Cycles in digraphs ? a survey,J. Graph Theory 5 (1981), 1-43. · Zbl 0458.05035 · doi:10.1002/jgt.3190050102
[3] S. Fortune, J. Hopcroft, andJ. Wyllie: The directed subgraph homeomorphism problem,Theoret. Comput. Sci. 10 (1980), 111-121. · Zbl 0419.05028 · doi:10.1016/0304-3975(80)90009-2
[4] L. Lovász: Problem, in: Proc. 5th British Conf. 1975,Congressus Numerantium XV. Utilitas Math. Publ. (1976), 696.
[5] C. Thomassen: 2-linked graphs,Europ. J. Combinatorics 1 (1980), 371-378. · Zbl 0457.05044
[6] C. Thomassen: Connectivity in tournaments, in:Graph Theory and Combinatorics (B. Bollobás, ed.). Academic Press (1984), 305-313.
[7] C. Thomassen: Configurations in graphs of large minimum degree, connectivity or chromatic number, in: Proc. 3rd Internat. Conf. on Combinatorial Mathematics, New York 1985,Ann. of the New York Acad. Sci. Vol.555 (1989), 402-412.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.