TY - JOUR
AU - Yan, Gui-Ying
AB - Let ℓ>r⩾3\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\ell >r\geqslant 3$$\end{document}. Given a 2-graph F, the expansion F(r)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$F^{(r)}$$\end{document} of F is an r-graph obtained from F by adding r-2\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$r-2$$\end{document} new vertices into each edge. When F is a clique of order ℓ\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\ell $$\end{document}, the Turán number ex(n,F(r))\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\textrm{ex}(n, F^{(r)})$$\end{document} was first asymptotically determined by Mubayi (J Comb Theory Ser B 96:122–134, 2006) and exactly computed by Pikhurko (J Comb Theory Ser B 103:220–225, 2013). Let Fk,ℓ\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$F_{k,\ell }$$\end{document} be the 2-graph on (ℓ-1)k+1\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$(\ell -1)k+1$$\end{document} vertices consisting of k cliques of order ℓ\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\ell $$\end{document} intersecting at exactly one vertex. We determine the exact Turán number ex(n,Fk,ℓ(3))\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\textrm{ex}(n, F_{k,\ell }^{(3)})$$\end{document} for all ℓ>3\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\ell >3$$\end{document}, k⩾1\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$k\geqslant 1$$\end{document} and sufficiently large n, as well as the corresponding extremal graphs.
TI - Turán Numbers of Expanded Intersecting Cliques in 3-graphs
JF - Journal of the Operations Research Society of China
DO - 10.1007/s40305-022-00451-3
DA - 2024-12-01
UR - https://www.deepdyve.com/lp/springer-journals/tur-n-numbers-of-expanded-intersecting-cliques-in-3-graphs-bb0p3VTp6f
SP - 952
EP - 964
VL - 12
IS - 4
DP - DeepDyve
ER -