A note on possible density and diameter of countere xamples to the Seymour’s second neighborhood conjecture

• Autorzy: Zelenskiy Oleksiy , Darmosiuk Valentyna , Nalivayko Illia

Identyfikatory

DOI

10.7494/OpMath.2021.41.4.601

• Języki publikacji: EN

Abstrakty

EN

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

Słowa kluczowe

EN

graph theory; Seymour’s second neighborhood conjecture; density of graph; diameter of graph

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2021
• Tom: Vol. 41, no. 4
• Strony: 601--605
• Opis fizyczny: BIbliogr. 3 poz.

Twórcy

autor

Zelenskiy Oleksiy

• Kamyanets-Podilsky Ivan Ohienko National University Department of Physics and Mathematics Ohienko Str. 61, 32 300, Kamianets-Podilsky, Ukraine

autor

Darmosiuk Valentyna

• V.O. Sukhomlynskyi Mykolaiv National University Department of Physics and Mathematics Nikolska Str. 24, Mykolaiv 54 001, Ukraine

autor

Nalivayko Illia

• 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).