Luyining Gan

activity

20202026

most citedHamiltonicity in Cherry-quasirandom 3-graphs

1 citations · 2 across the 15 of their papers we have counts for

collaborators

15 papers

math.CO2026

Decision problem for Hamilton $2$ -cycles in $4$ -graphs

Luyining Gan, Jie Han, Bin Wang

A $4$ -uniform $2$ -cycle in a $4$ -uniform hypergraph of length $t$ is a cyclic ordering of $2 t$ vertices $v_{1} v_{2} \dots v_{2 t} v_{1}$ such that $v_{2 i + 1} v_{2 i + 2} v_{2 i + 3} v_{2 i + 4}$ are ed…

math.CO2026

Note on the codegree version of the Erdős--Ko--Rado theorem

Luyining Gan, Jie Han, Seonghyuk Im

Kupavskii proved a codegree version of the Erdős--Ko--Rado theorem by showing that for an intersecting family $F \subseteq (k [ n ])$ with $n \geq 2 k + 3 d / (1 - d / k)$ , t…

math.CO2026

Exact minimum co-degree conditions for $ℓ$ -Hamiltonicity in hypergraphs

Luyining Gan, Jie Han, Huan Xu

Suppose $1 \leq ℓ < k$ such that $(k - ℓ) ∤ k$ . Given an $n$ -vertex $k$ -uniform hypergraph $H$ , for all $k /2 < ℓ < 3 k /4$ and sufficiently large $n\in (k-\ell)\mathbb N…

math.FA2023

Order Relations of the Wasserstein mean and the spectral geometric mean

Luyining Gan, Huajun Huang

On the space of positive definite matrices, several operator means are popular and have been studied extensively. In this paper, we investigate the near order and the Löwner order…

math.CO2023

A parameterized algorithm for $K_{r}$ -factors in graphs of high minimum degree

Luyining Gan, Jie Han, Jie Hu

A $K_{r}$ -factor of a graph $G$ is a collection of vertex-disjoint $r$ -cliques covering $V (G)$ . We prove the following algorithmic version of the classical Hajnal--Szemerédi Theorem…

math.FA2023

Weak log-majorization between the geometric and Wasserstein means

Luyining Gan, Sejong Kim

There exist lots of distinct geometric means on the cone of positive definite Hermitian matrices such as the metric geometric mean, spectral geometric mean, log-Euclidean mean and…

math.CO2022

Zero Forcing with Random Sets

Bryan Curtis, Luyining Gan, Jamie Haddock +2

Given a graph $G$ and a real number $0 \leq p \leq 1$ , we define the random set $B_{p} (G) \subset V (G)$ by including each vertex independently and with probability $p$ . We investigate the…

math.FA2022

Revisit on spectral geometric mean

Luyining Gan, Sejong Kim

In this paper we introduce the limit, unique solution of the nonlinear equations, geodesic property, tolerance relations and pinch on the spectral geometric mean for two positive d…

math.CO2022

Complementary Vanishing Graphs

Craig Erickson, Luyining Gan, Jürgen Kritschgau +2

Given a graph $G$ with vertices ${v_{1}, \dots, v_{n}}$ , we define $S (G)$ to be the set of symmetric matrices $A = [a_{i, j}]$ such that for $i \neq = j$ we have $a_{i, j} \neq = 0$ if…

math.CO2022

On the Keevash-Knox-Mycroft Conjecture

Luyining Gan, Jie Han

Given $1 \leq ℓ < k$ and $δ \geq 0$ , let $PM (k, ℓ, δ)$ be the decision problem for the existence of perfect matchings in $n$ -vertex $k$ -uniform hypergraphs with minimum $\el…

math.CO2021

Large $Y_{k, b}$ -tilings and Hamilton $ℓ$ -cycles in $k$ -uniform hypergraphs

Luyining Gan, Jie Han, Lin Sun +1

Let $Y_{3, 2}$ be the $3$ -uniform hypergraph with two edges intersecting in two vertices. Our main result is that any $n$ -vertex 3-uniform hypergraph with at least $\binom{n}{3} - \…

math.RA2021★ 1 cited

Inequalities and limits of weighted spectral geometric mean

Luyining Gan, Tin-Yau Tam

We establish some new properties of spectral geometric mean. In particular, we prove a log majorization relation between $(B^{t s /2} A^{(1 - t) s} B^{t s /2})^{1/ s}$ and the $t…

math.RA2021

On two geometric means and sum of adjoint orbits

Luyining Gan, Xuhua Liu, Tin-Yau Tam

In this paper, we study the metric geometric mean introduced by Pusz and Woronowicz and the spectral geometric mean introduced by Fiedler and Pták, originally for positive definite…

math.DG2021

Curvature of matrix and reductive Lie groups

Luyining Gan, Ming Liao, Tin-Yau Tam

In this paper, we give a simple formula for sectional curvatures on the general linear group, which is also valid for many other matrix groups. Similar formula is given for a reduc…

math.CO2020★ 1 cited

Hamiltonicity in Cherry-quasirandom 3-graphs

Luyining Gan, Jie Han

We show that for any fixed $α > 0$ , cherry-quasirandom 3-graphs of positive density and sufficiently large order $n$ with minimum vertex degree $α (2 n)$ have a tight Hamilton cyc…

Decision problem for Hamilton 2-cycles in 4-graphs

Note on the codegree version of the Erdős--Ko--Rado theorem

Exact minimum co-degree conditions for ℓ-Hamiltonicity in hypergraphs

Order Relations of the Wasserstein mean and the spectral geometric mean

A parameterized algorithm for Kr​-factors in graphs of high minimum degree

Weak log-majorization between the geometric and Wasserstein means

Zero Forcing with Random Sets

Revisit on spectral geometric mean

Complementary Vanishing Graphs

On the Keevash-Knox-Mycroft Conjecture

Large Yk,b​-tilings and Hamilton ℓ-cycles in k-uniform hypergraphs

Inequalities and limits of weighted spectral geometric mean

On two geometric means and sum of adjoint orbits

Curvature of matrix and reductive Lie groups

Hamiltonicity in Cherry-quasirandom 3-graphs

Decision problem for Hamilton $2$ -cycles in $4$ -graphs

Exact minimum co-degree conditions for $ℓ$ -Hamiltonicity in hypergraphs

A parameterized algorithm for $K_{r}$ -factors in graphs of high minimum degree

Large $Y_{k, b}$ -tilings and Hamilton $ℓ$ -cycles in $k$ -uniform hypergraphs