CHAN, Timothy Fong Nam, Andrzej GRZESIK, Daniel KRÁĽ a Jonathan Andrew NOEL. CYCLES OF LENGTH THREE AND FOUR IN TOURNAMENTS. Acta Mathematica Universitatis Comenianae. Bratislava: Comenius University, 2019, roč. 88, č. 3, s. 533-539. ISSN 0231-6986. |
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@article{1646921, author = {Chan, Timothy Fong Nam and Grzesik, Andrzej and Kráľ, Daniel and Noel, Jonathan Andrew}, article_location = {Bratislava}, article_number = {3}, keywords = {Tournaments; extremal combinatorics}, language = {eng}, issn = {0231-6986}, journal = {Acta Mathematica Universitatis Comenianae}, title = {CYCLES OF LENGTH THREE AND FOUR IN TOURNAMENTS}, url = {http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/1222}, volume = {88}, year = {2019} }
TY - JOUR ID - 1646921 AU - Chan, Timothy Fong Nam - Grzesik, Andrzej - Kráľ, Daniel - Noel, Jonathan Andrew PY - 2019 TI - CYCLES OF LENGTH THREE AND FOUR IN TOURNAMENTS JF - Acta Mathematica Universitatis Comenianae VL - 88 IS - 3 SP - 533-539 EP - 533-539 PB - Comenius University SN - 02316986 KW - Tournaments KW - extremal combinatorics UR - http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/1222 L2 - http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/1222 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. ER -
CHAN, Timothy Fong Nam, Andrzej GRZESIK, Daniel KRÁĽ a Jonathan Andrew NOEL. CYCLES OF LENGTH THREE AND FOUR IN TOURNAMENTS. \textit{Acta Mathematica Universitatis Comenianae}. Bratislava: Comenius University, 2019, roč.~88, č.~3, s.~533-539. ISSN~0231-6986.
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