Hongliang Lu
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The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
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Research Interests
Hongliang Lu has a total of 57 co-authors. Here are the top co-authors by number of shared publications:
Mingyang Guo
School of Mathematics and Statistics Zhengzhou University Zhengzhou Henan China
7 shared publications- Qinglin Yu
School of Science Xi'an Polytechnic University Xi'an China
6 shared publications - Xingxing Yu
School of Mathematics, Georgia Institute of Technology, Atlanta, USA
6 shared publications - Yuqing Lin
The University of Newcastle
5 shared publications - Jie Ma
School of Mathematical Sciences, University of Science and Technology of China, Hefei, China
4 shared publications Xinxin Ma
4 shared publications
Latest Publications
- 16 April 2026
- Published by Springer Nature in Science China Mathematics
- p. 1-24
Discrepancies of perfect matchings in hypergraphs
- 16 April 2026
- Published by Springer Nature in Science China Mathematics
- p. 1-24
Discrepancies of perfect matchings in hypergraphs
- Open Access
Towards the Erdős matching conjecture for 4-uniform hypergraphs: stability and applications
A famous conjecture of Erdős asserts that for $k\ge 3$, the maximum number of edges in an $n$-vertex $k$-uniform hypergraph without $s+1$ pairwise disjoint edges is $\max\{\binom{n}{k}-\binom{n-s}{k},\binom{sk+k-1}{k}\}$. This problem has been central in extremal combinatorics, with substantial progress in the literature, including a complete solution for $k=3$ due to the first author. In this paper, we make progress towards the $4$-uniform case, proving the conjecture for $n\ge 5s$ and sufficiently large $n$, thereby taking a first step analogous to the $3$-uniform case. The main technical contribution is a stability result of independent interest. We further apply this stability to resolve two new instances of conjectures on the minimum $d$-degree threshold for matchings in $5$- and $6$-uniform hypergraphs, in a strengthened form.Open AccessTowards the Erdős matching conjecture for 4-uniform hypergraphs: stability and applications
A famous conjecture of Erdős asserts that for $k\ge 3$, the maximum number of edges in an $n$-vertex $k$-uniform hypergraph without $s+1$ pairwise disjoint edges is $\max\{\binom{n}{k}-\binom{n-s}{k},\binom{sk+k-1}{k}\}$. This problem has been central in extremal combinatorics, with substantial progress in the literature, including a complete solution for $k=3$ due to the first author. In this paper, we make progress towards the $4$-uniform case, proving the conjecture for $n\ge 5s$ and sufficiently large $n$, thereby taking a first step analogous to the $3$-uniform case. The main technical contribution is a stability result of independent interest. We further apply this stability to resolve two new instances of conjectures on the minimum $d$-degree threshold for matchings in $5$- and $6$-uniform hypergraphs, in a strengthened form. - 18 February 2026
- Published by Wiley in Journal of Graph Theory
- Vol. 112 (1) , 5-14
A Stability Result for Almost Perfect Matchings
Let be three integers and be a sufficiently small positive number such that , , and . A ‐graph is called non‐trivial if it has no isolated vertex. In this paper, we determine the maximum number of edges in a non‐trivial ‐graph with vertices and matching number at most . This result confirms a conjecture proposed by Frankl (On non‐trivial families without a perfect matching, European J. Combin ., 84 (2020), 103044) for the case when is sufficiently large.
- 18 February 2026
- Published by Wiley in Journal of Graph Theory
- Vol. 112 (1) , 5-14
A Stability Result for Almost Perfect Matchings
Let be three integers and be a sufficiently small positive number such that , , and . A ‐graph is called non‐trivial if it has no isolated vertex. In this paper, we determine the maximum number of edges in a non‐trivial ‐graph with vertices and matching number at most . This result confirms a conjecture proposed by Frankl (On non‐trivial families without a perfect matching, European J. Combin ., 84 (2020), 103044) for the case when is sufficiently large.
- Open Access
Rainbow matchings in edge-colored graphs
Let $G$ be an edge-colored graph. We use $e(G)$ and $c(G)$ to denote the number of edges and colors in $G$, respectively. A subgraph $H$ is called rainbow if $c(H)=e(H)$. Li et al. (European J. Combin., 36 (2014), 453-459) proved that every edge-colored graph on $n$ vertices with $e(G)+c(G) \geq n(n+1)/2$ contains rainbow triangles. Later, Xu et al. (European J. Combin., 54 (2016), 193-200) generalized the previous results concerning rainbow triangles to rainbow cliques $Kr$, where $r\geq 4$. In this paper, we consider the existence of rainbow matchings of size $k$ in general edge-colored graphs $G$ under the condition of $e(G)+c(G)$, and the condition in our result is tight.Open AccessRainbow matchings in edge-colored graphs
Let $G$ be an edge-colored graph. We use $e(G)$ and $c(G)$ to denote the number of edges and colors in $G$, respectively. A subgraph $H$ is called rainbow if $c(H)=e(H)$. Li et al. (European J. Combin., 36 (2014), 453-459) proved that every edge-colored graph on $n$ vertices with $e(G)+c(G) \geq n(n+1)/2$ contains rainbow triangles. Later, Xu et al. (European J. Combin., 54 (2016), 193-200) generalized the previous results concerning rainbow triangles to rainbow cliques $Kr$, where $r\geq 4$. In this paper, we consider the existence of rainbow matchings of size $k$ in general edge-colored graphs $G$ under the condition of $e(G)+c(G)$, and the condition in our result is tight. - 17 February 2025
- Published by Elsevier in Discrete Mathematics
- Vol. 348 (6)
A characterization on (g,f)-parity orientations
- 17 February 2025
- Published by Elsevier in Discrete Mathematics
- Vol. 348 (6)
A characterization on (g,f)-parity orientations
- 5 June 2024
- Published by Springer Nature in Acta Mathematicae Applicatae Sinica, English Series
- Vol. 40 (3) , 656-664
A Degree Condition for Graphs Having All (a, b)-parity Factors
- 5 June 2024
- Published by Springer Nature in Acta Mathematicae Applicatae Sinica, English Series
- Vol. 40 (3) , 656-664
A Degree Condition for Graphs Having All (a, b)-parity Factors
- Open Access
A stability result for almost perfect matchings
Let $n,k,s$ be three integers and $β$ be a sufficiently small positive number such that $k\geq 3$, $0<1/n\ll β\ll 1/k$ and $ks+k\leq n\leq (1+β)ks+k-2$. A $k$-graph is called non-trivial if it has no isolated vertex. In this paper, we determine the maximum number of edges in a non-trivial $k$-graph with $n$ vertices and matching number at most $s$. This result confirms a conjecture proposed by Frankl (On non-trivial families without a perfect matching, \emph{European J. Combin.}, \textbf{84} (2020), 103044) for the case when $s$ is sufficiently large.Open AccessA stability result for almost perfect matchings
Let $n,k,s$ be three integers and $β$ be a sufficiently small positive number such that $k\geq 3$, $0<1/n\ll β\ll 1/k$ and $ks+k\leq n\leq (1+β)ks+k-2$. A $k$-graph is called non-trivial if it has no isolated vertex. In this paper, we determine the maximum number of edges in a non-trivial $k$-graph with $n$ vertices and matching number at most $s$. This result confirms a conjecture proposed by Frankl (On non-trivial families without a perfect matching, \emph{European J. Combin.}, \textbf{84} (2020), 103044) for the case when $s$ is sufficiently large. - Open Access
A characterization on $(g,f)$-parity orientations
Let $G$ be a graph and $g,f:V(G)\to2^N$ be two set functions such that $g(v)\le f(v)$ and $g(v)\equiv f(v)\pmod 2$ for every $v\in V(G)$. An orientation $O$ of $G$ is called a $(g,f)$-parity orientation if $g(v)\le d^+_O(v)\le f(v)$ and $g(v)\equiv d^+_O(v)\pmod 2$ for every $v\in V(G)$. In this paper, we give a Tutte-type characterization for a graph to have a $(g,f)$-parity orientation.Open AccessA characterization on $(g,f)$-parity orientations
Let $G$ be a graph and $g,f:V(G)\to2^N$ be two set functions such that $g(v)\le f(v)$ and $g(v)\equiv f(v)\pmod 2$ for every $v\in V(G)$. An orientation $O$ of $G$ is called a $(g,f)$-parity orientation if $g(v)\le d^+_O(v)\le f(v)$ and $g(v)\equiv d^+_O(v)\pmod 2$ for every $v\in V(G)$. In this paper, we give a Tutte-type characterization for a graph to have a $(g,f)$-parity orientation. - Open Access
Eigenvalues and factors: a survey
A factor of a graph is a spanning subgraph satisfying some given conditions. An earlier survey of factors can be traced back to the Akiyama and Kano [J. Graph Theory, 1985, 9: 1-42] in which they described the characterization of factors in (bipartite) graphs and digraphs, respectively. Soon after, Kouider and Vestergaard summarized the findings related to connected factors [Graphs Combin., 2005, 21(1): 1-26]. Plummer extended the aforementioned research by providing a comprehensive overview of progress made in the study of graph factors and factorization from 1985 to 2003 [Discrete Math., 2007, 7-8: 791-821]. In this paper, we aim to summarize the relevant results regarding factors from the perspective of eigenvalues.
Open AccessEigenvalues and factors: a survey
A factor of a graph is a spanning subgraph satisfying some given conditions. An earlier survey of factors can be traced back to the Akiyama and Kano [J. Graph Theory, 1985, 9: 1-42] in which they described the characterization of factors in (bipartite) graphs and digraphs, respectively. Soon after, Kouider and Vestergaard summarized the findings related to connected factors [Graphs Combin., 2005, 21(1): 1-26]. Plummer extended the aforementioned research by providing a comprehensive overview of progress made in the study of graph factors and factorization from 1985 to 2003 [Discrete Math., 2007, 7-8: 791-821]. In this paper, we aim to summarize the relevant results regarding factors from the perspective of eigenvalues.
- Open Access
A characterization on orientations of graphs avoiding given lists on out-degrees
Let $G$ be a graph and $F:V(G)\to2^N$ be a set function. The graph $G$ is said to be \emph{F-avoiding} if there exists an orientation $O$ of $G$ such that $d^+_O(v)\notin F(v)$ for every $v\in V(G)$, where $d^+_O(v)$ denotes the out-degree of $v$ in the directed graph $G$ with respect to $O$. In this paper, we give a Tutte-type good characterization to decide the $F$-avoiding problem when for every $v\in V(G)$, $|F(v)|\leq \frac{1}{2}(d_G(v)+1)$ and $F(v)$ contains no two consecutive integers. Our proof also gives a simple polynomial algorithm to find a desired orientation. As a corollary, we prove the following result: if for every $v\in V(G)$, $|F(v)|\leq \frac{1}{2}(d_G(v)+1)$ and $F(v)$ contains no two consecutive integers, then $G$ is $F$-avoiding. This partly answers a problem proposed by Akbari et. al.(2020)Open AccessA characterization on orientations of graphs avoiding given lists on out-degrees
Let $G$ be a graph and $F:V(G)\to2^N$ be a set function. The graph $G$ is said to be \emph{F-avoiding} if there exists an orientation $O$ of $G$ such that $d^+_O(v)\notin F(v)$ for every $v\in V(G)$, where $d^+_O(v)$ denotes the out-degree of $v$ in the directed graph $G$ with respect to $O$. In this paper, we give a Tutte-type good characterization to decide the $F$-avoiding problem when for every $v\in V(G)$, $|F(v)|\leq \frac{1}{2}(d_G(v)+1)$ and $F(v)$ contains no two consecutive integers. Our proof also gives a simple polynomial algorithm to find a desired orientation. As a corollary, we prove the following result: if for every $v\in V(G)$, $|F(v)|\leq \frac{1}{2}(d_G(v)+1)$ and $F(v)$ contains no two consecutive integers, then $G$ is $F$-avoiding. This partly answers a problem proposed by Akbari et. al.(2020)