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@article{1646916, author = {Hubai, Tamás and Kráľ, Daniel and Parczyk, Olaf and Person, Yuri}, article_location = {Bratislava}, article_number = {3}, keywords = {Quasirandom graphs; Forcing Conjecture}, language = {eng}, issn = {0231-6986}, journal = {Acta Mathematica Universitatis Comenianae}, title = {MORE NON-BIPARTITE FORCING PAIRS}, url = {http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/1279}, volume = {88}, year = {2019} }
TY - JOUR ID - 1646916 AU - Hubai, Tamás - Kráľ, Daniel - Parczyk, Olaf - Person, Yuri PY - 2019 TI - MORE NON-BIPARTITE FORCING PAIRS JF - Acta Mathematica Universitatis Comenianae VL - 88 IS - 3 SP - 819-825 EP - 819-825 PB - Comenius University SN - 02316986 KW - Quasirandom graphs KW - Forcing Conjecture UR - http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/1279 L2 - http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/1279 N2 - We study pairs of graphs (H-1, H-2) such that every graph with the densities of H-1 and H-2 close to the densities of H-1 and H-2 in a random graph is quasirandom; such pairs (H-1, H-2) are called forcing. Non-bipartite forcing pairs were first discovered by Conlon, Han, Person and Schacht [Weak quasi-randomness for uniform hypergraphs, Random Structures Algorithms 40 (2012), no. 1, 1-38]: they showed that (K-t, F) is forcing where F is the graph that arises from K-t by iteratively doubling its vertices and edges in a prescribed way t times. Reiher and Schacht [Forcing quasirandomness with triangles, Forum of Mathematics, Sigma. Vol. 7, 2019] strengthened this result for t = 3 by proving that two doublings suffice and asked for the minimum number of doublings needed for t > 3. We show that [t + 1)/2] doublings always suffice. ER -
HUBAI, Tamás, Daniel KRÁĽ, Olaf PARCZYK and Yuri PERSON. MORE NON-BIPARTITE FORCING PAIRS. \textit{Acta Mathematica Universitatis Comenianae}. Bratislava: Comenius University, 2019, vol.~88, No~3, p.~819-825. ISSN~0231-6986.
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