On the maximum number of r-cliques in graphs free of complete r-partite subgraphs
arxiv(2024)
摘要
We estimate the maximum possible number of cliques of size r in an
n-vertex graph free of a fixed complete r-partite graph K_s_1, s_2,
…, s_r. By viewing every r-clique as a hyperedge, the upper bound on
the Turán number of the complete r-partite hypergraphs gives the upper
bound O(n^r - 1/∏_i=1^r-1s_i). We improve this to
o(n^r - 1/∏_i=1^r-1s_i). The main tool in our proof
is the graph removal lemma. We also provide several lower bound constructions.
更多查看译文
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络
Chat Paper
正在生成论文摘要