References & Citations
Mathematics > Combinatorics
Title: A step towards a general density Corrádi--Hajnal Theorem
(Submitted on 20 Feb 2023 (v1), last revised 27 Feb 2023 (this version, v2))
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 Corr\'{a}di--Hajnal Theorem~\cite{CH63}.
Submission history
From: Xizhi Liu [view email][v1] Mon, 20 Feb 2023 09:12:10 GMT (37kb)
[v2] Mon, 27 Feb 2023 11:19:56 GMT (38kb)
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