Pith. sign in

REVIEW 4 cited by

A step towards a general density Corr\'{a}di--Hajnal Theorem

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2302.09849 v2 pith:YE23R543 submitted 2023-02-20 math.CO

Jianfeng Hou , Heng Li , Xizhi Liu , Long-Tu Yuan , Yixiao Zhang This is my paper · ORCID
classification math.CO
keywords citegeneralgraphsresultsapproachcorrdensitydi--hajnal
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
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}.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. The Tur\'an density of the tight 5-cycle minus one edge

    math.CO 2024-12 accept novelty 8.0 of 10

    The Turán density of the tight 5-cycle minus one edge is 1/4, resolving a 2011 conjecture and extending the result to all cycle lengths not divisible by 3.

  2. The Tur\'{a}n density of short tight cycles

    math.CO 2025-06 accept novelty 7.0 of 10

    The Turán density of every 3-uniform tight cycle of length ℓ≥7 with ℓ not divisible by 3, and of the pair {C4^3,C5^3}, is exactly 2√3−3.

  3. Tiling $H$ in dense graphs

    math.CO 2025-01 conditional novelty 7.0 of 10

    The asymptotic maximum number of edges in a graph with H-matching number below beta n is determined for the H-shaped tree, refuting Lang's conjecture.

  4. Density Hajnal--Szemer\'{e}di theorem for cliques of size four

    math.CO 2025-01 conditional novelty 7.0 of 10

    For large n and any k ≤ n/4, the maximum number of edges in an n-vertex graph with no k+1 disjoint K4's is asymptotically Ξ(n,k), a piecewise quadratic with five regimes.

Pith tools