禁用C_(4)的IC-可平面图中C_(k)的最大个数  

The Maximum Number of C_(k) in a C_(4)-free IC-planar Graph

作　　者：王祎 兰永新 徐常青[1] WANG Yi;LAN Yongxin;XU Changqing(School of Science,Hebei University of Technology,Tianjin,300401,P.R.China)

机构地区：[1]河北工业大学理学院,天津300401

出　　处：《数学进展》2023年第5期789-794,共6页Advances in Mathematics（China）

基　　金：国家自然科学基金(Nos.12001154,12071260);天津市共建高校专项资金(No.280000307);河北省自然科学基金(No.A2021202025)

摘　　要：给定图G和H,如果图G不包含图H作为子图,则称图G是禁用H的.用ex_(ICP)(n,F,H)表示在所有禁用H且顶点数为n的IC-可平面图中,含与F同构的子图的最大个数.本文证明了对任意的k≥5,当n充分大时,有ex_(ICP)(n,C_(k),C_(4))=Θ(n^([k/3])).Let G and H be two graphs.A graph G is H-free if G contains no H as a subgraph.Let ex_(ICP)(n,F,H)denote the maximum number of copies of F in an H-free ICplanar graph of order n.In this paper,we prove that ex_(ICP)(n,C_(k),C_(4))=Θ(n^([k/3]))for all k≥5 and sufficiently large n.

关 键 词：广义Turán数 IC-可平面图 k-圈 

分 类 号：O157.5[理学—数学]