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Abstrakty
Seymour’s second neighborhood conjecture states that every simple digraph without loops or 2-cycles contains a vertex whose second neighborhood is at least as large as its first. In this paper we show, that from falsity of Seymour’s second neighborhood conjecture it follows that there exist strongly-connected counterexamples with both low and high density (dense and sparse graph). Moreover, we show that if there is a counterexample to conjecture, then it is possible to construct counterexample with any diameter k ≥ 3
Czasopismo
Rocznik
Tom
Strony
601--605
Opis fizyczny
BIbliogr. 3 poz.
Twórcy
autor
- Kamyanets-Podilsky Ivan Ohienko National University Department of Physics and Mathematics Ohienko Str. 61, 32 300, Kamianets-Podilsky, Ukraine
autor
- V.O. Sukhomlynskyi Mykolaiv National University Department of Physics and Mathematics Nikolska Str. 24, Mykolaiv 54 001, Ukraine
autor
- Kamyanets-Podilsky Gymnasium 14 Heroes of the Heavenly Hundred Str. 17 32 300, Kamianets-Podilsky, Ukraine
Bibliografia
- [1] N. Dean, B.J. Latka, Squaring the tournament - an open problem, [in:] Proceedings of the Twenty-sixth Southeastern International Conference on Combinatorics, Graph Theory and Computing (Boca Raton, FL, 1995) 109 (1995), 73-80.
- [2] D.C. Fisher, Squaring a tournament: A proof of Dean’s conjecture, J. Graph Theory 23 (1996), no. 1, 43-48.
- [3] Y. Kaneko, S.C. Locke, The minimum degree approach for Paul Seymour’s distance 2 conjecture, [in:] Proceedings of the Thirty-second Southeastern International Conference on Combinatorics, Graph Theory and Computing (Baton Rouge, LA, 2001) 148 (2001), 201-206.
Uwagi
Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-41f7a0a6-fa97-462d-ad7e-a1f4135f89fd