1. A step towards a general density Corrádi--Hajnal Theorem
- Author
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Hou, Jianfeng, Li, Heng, Liu, Xizhi, Yuan, Long-Tu, and Zhang, Yixiao
- Subjects
FOS: Mathematics ,Combinatorics (math.CO) - Abstract
For a nondegenerate $r$-graph $F$, large $n$, and $t$ in the regime $[0, c_{F} n]$, where $c_F>0$ is a constant depending only on $F$, we present a general approach for determining the maximum number of edges in an $n$-vertex $r$-graph that does not contain $t+1$ vertex-disjoint copies of $F$. In fact, our method results in a rainbow version of the above result and includes a characterization of the extremal constructions. Our approach applies to many well-studied hypergraphs (including graphs) such as the edge-critical graphs, the Fano plane, the generalized triangles, hypergraph expansions, the expanded triangles, and hypergraph books. Our results extend old results of Simonovits~\cite{SI68} and Moon~\cite{Moon68} on complete graphs and can be viewed as a step towards a general density version of the classical Corrádi--Hajnal Theorem~\cite{CH63}., corrected some typo and added a theorem (THM 2.7) about expanded Erdos-Sos trees
- Published
- 2023
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