点不交团的Turán数献给刘桂真教授80寿辰  

Turán numbers of vertex-disjoint copies of cliques

作　　者：严子龙 张义冉 彭岳建[1] Zilong Yan;Yiran Zhang;Yuejian Peng

机构地区：[1]湖南大学数学学院,长沙410082

出　　处：《中国科学：数学》2024年第11期1851-1864,共14页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:11931002);中国博士后科学基金(批准号:2023M741131)资助项目。

摘　　要：Turán(1941)确定了当p≥3时Turán数ex(n,K_(p))的精确值并给出了唯一极图.当n充分大时,Moon(1968)和Simonovits(1968)分别独立地确定Turán数ex(n,k K_(p))的值并证明了K_(k-1)∨T_(p-1)(n-k+1)是唯一的极图.当n≥2p且p≥3时,Chen等(2022)确定了ex(n,2K_(p))的精确值.对所有n≥3p,本文给出ex(n,3K_(p))的精确值并能确定3K_(p)的极图.在n充分大的条件下,确定Turán数ex(n,k K_(p))无法应用到Ramsey数问题中,本文的结果可应用到确定路径对3K_(p)的Ramsey数.Turan(1941)determined the Turán number ex(n;K_(p))for p≥3.Moon(1968)and Simonovits(1968)independently determined the Turán number ex(n,kK_(p))for n sufficiently large,and determined that K_(k-1)∨T_(p-1)(n-k+1))is the unique extremal graph for kK_(p).Chen et al.(2022)showed the exact value of ex(n,2K_(p))for all n>2p and p≥3.In this paper,we determine ex(n;3K_(p))for all n>3p and determine extremal graphs for 3K_(p).Determining Turán numbers ex(n;F)under the condition n large enough cannot be applied to corresponding Ramsey numbers.The result in this paper can be applied to determining the Ramsey number R(3K_(p);P_(t))for t≥6 and p≥3.

关 键 词：Turán数团 Hajanl-Szemerédi定理 

分 类 号：O157.5[理学—数学]