Let l>r≥3.Given a 2-graph F,the expansion E^((r))of F is an r-graph obtained from F by adding r-2 new vertices into each edge.When F is a clique of order l,the Turán number ex(n,F^((r)))was first asymptotical...Let l>r≥3.Given a 2-graph F,the expansion E^((r))of F is an r-graph obtained from F by adding r-2 new vertices into each edge.When F is a clique of order l,the Turán number ex(n,F^((r)))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 F_(k,l)be the 2-graph on(l-1)k+1 vertices consisting of k cliques of order l intersecting at exactly one vertex.We determine the exact Turán number ex(n,F_(k,l)^((3)))for all l>3,k≥1,and sufficiently large n,as well as the corresponding extremal graphs.展开更多
基金supported in part by the National Natural Science Foundation of China(Nos.11901292,11631014).
文摘Let l>r≥3.Given a 2-graph F,the expansion E^((r))of F is an r-graph obtained from F by adding r-2 new vertices into each edge.When F is a clique of order l,the Turán number ex(n,F^((r)))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 F_(k,l)be the 2-graph on(l-1)k+1 vertices consisting of k cliques of order l intersecting at exactly one vertex.We determine the exact Turán number ex(n,F_(k,l)^((3)))for all l>3,k≥1,and sufficiently large n,as well as the corresponding extremal graphs.
基金Supported by NNSF of China (Grant No. 10271105) Foundation of Education Ministry of Fujian Province (Grant No. AJ03147) Foundation of Science and Technology Ministry of Fujian Province (Grant No. 2003J036)
