CHAN, Timothy F. N., Andrzej GRZESIK, Daniel KRÁĽ and Jonathan A. NOEL. Cycles of length three and four in tournaments. Journal of Combinatorial Theory, Series A. SAN DIEGO: ACADEMIC PRESS INC ELSEVIER SCIENCE, 2020, vol. 175, No 105276, p. 1-23. ISSN 0097-3165. Available from: https://dx.doi.org/10.1016/j.jcta.2020.105276. |
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@article{1759844, author = {Chan, Timothy F. N. and Grzesik, Andrzej and Kráľ, Daniel and Noel, Jonathan A.}, article_location = {SAN DIEGO}, article_number = {105276}, doi = {http://dx.doi.org/10.1016/j.jcta.2020.105276}, keywords = {Tournaments; Cycles; Extremal combinatorics}, language = {eng}, issn = {0097-3165}, journal = {Journal of Combinatorial Theory, Series A}, title = {Cycles of length three and four in tournaments}, url = {http://dx.doi.org/10.1016/j.jcta.2020.105276}, volume = {175}, year = {2020} }
TY - JOUR ID - 1759844 AU - Chan, Timothy F. N. - Grzesik, Andrzej - Kráľ, Daniel - Noel, Jonathan A. PY - 2020 TI - Cycles of length three and four in tournaments JF - Journal of Combinatorial Theory, Series A VL - 175 IS - 105276 SP - 1-23 EP - 1-23 PB - ACADEMIC PRESS INC ELSEVIER SCIENCE SN - 00973165 KW - Tournaments KW - Cycles KW - Extremal combinatorics UR - http://dx.doi.org/10.1016/j.jcta.2020.105276 N2 - Linial and Morgenstern conjectured that, among all n-vertex tournaments with d((n)(3)) cycles of length three, the number of cycles of length four is asymptotically minimized by a random blow-up of a transitive tournament with all but one part of equal size and one smaller part. We prove the conjecture for d >= 1/36 by analyzing the possible spectrum of adjacency matrices of tournaments. We also demonstrate that the family of extremal examples is broader than expected and give its full description for d >= 1/16. (C) 2020 Elsevier Inc. All rights reserved. ER -
CHAN, Timothy F. N., Andrzej GRZESIK, Daniel KRÁĽ and Jonathan A. NOEL. Cycles of length three and four in tournaments. \textit{Journal of Combinatorial Theory, Series A}. SAN DIEGO: ACADEMIC PRESS INC ELSEVIER SCIENCE, 2020, vol.~175, No~105276, p.~1-23. ISSN~0097-3165. Available from: https://dx.doi.org/10.1016/j.jcta.2020.105276.
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