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Tetrahedron Conjecture in the -norm
Levente Bodnár, Wanfang Chen, Jinghua Deng +5
The famous Tetrahedron Conjecture of Turán from the 1940s asserts that the number of edges in an -vertex -graph without the tetrahedron, the complete -graph on four vertic…
Tight bounds towards Zarankiewicz problem in hypergraph
Guorong Gao, Jianfeng Hou, Shuping Huang +1
The classical Zarankiewicz problem, which concerns the maximum number of edges in a bipartite graph without a forbidden complete bipartite subgraph, motivates a direct analogue for…
Odd hypergraph Mantel theorems
Jianfeng Hou, Xizhi Liu, Yixiao Zhang +2
A classical result of Sidorenko (1989) shows that the Turán density of every -uniform hypergraph with three edges is bounded from above by . For even , this bound is tig…
Toward a rainbow Corrádi--Hajnal Theorem \RNum{1}
Deng Jinghua, Hou Jianfeng, Hu caiyun +1
We study an anti-Ramsey extension of the classical Corrádi--Hajnal Theorem: how many colors are needed to color the complete graph on vertices in order to guarantee a rainbow c…
On a refinement of the Ahlswede--Katona Theorem
Jianfeng Hou, Xizhi Liu, Yixiao Zhang
A classical theorem of Ahlswede and Katona determines the maximum density of the -edge star in a graph with a given edge density. Motivated by its application in hypergraph Turá…
Exact Turán number of the Fano plane in the -norm
Jianfeng Hou, Xizhi Liu, Yixiao Zhang
A classical object in hypergraph Turán theory is the Fano plane , the unique linear -graph on seven vertices with seven edges. The Turán density and exact Turán numb…
Turán density of tight cycles minus one edge in the -norm
Levente Bodnár, Jinghua Deng, Jianfeng Hou +2
The -uniform tight -cycle minus one edge is the -graph on vertices consisting of consecutive triples in the cyclic order. We show that f…
Max-Bisections of graphs without even cycles
Jianfeng Hou, Siwei Lin, Qinghou Zeng
For an integer , let be a graph with edges and without cycles of length . The pivotal Alon-Krivelevich-Sudakov Theorem on Max-Cuts states that has a biparti…
Density Hajnal--Szemerédi theorem for cliques of size four
Jianfeng Hou, Caiyun Hu, Xizhi Liu +1
The celebrated Corrádi--Hajnal Theorem~\cite{CH63} and the Hajnal--Szemerédi Theorem~\cite{HS70} determined the exact minimum degree thresholds for a graph on vertices to conta…