Xiaonan Liu

activity

20212026

χ

-binding functions for

t

-broom-free graphs

3 citations · 4 across the 7 of their papers we have counts for

collaborators

Showing 2021Show all

5 papers · 1 filter

math.CO2021

Planar Turán Numbers of Cycles: A Counterexample

Daniel W. Cranston, Bernard Lidický, Xiaonan Liu +1

The planar Turan number $ex_{P} (C_{ℓ}, n)$ is the largest number of edges in an $n$ -vertex planar graph with no $ℓ$ -cycle. For $ℓ \in {3, 4, 5, 6}$ , upper…

math.CO2021★ 3 cited

Polynomial $χ$ -binding functions for $t$ -broom-free graphs

Xiaonan Liu, Joshua Schroeder, Zhiyu Wang +1

For any positive integer $t$ , a \emph{ $t$ -broom} is a graph obtained from $K_{1, t + 1}$ by subdividing an edge once. In this paper, we show that, for graphs $G$ without induced $t$ -b…

math.CO2021

Counting Hamiltonian cycles in planar triangulations

Xiaonan Liu, Zhiyu Wang, Xingxing Yu

Hakimi, Schmeichel, and Thomassen in 1979 conjectured that every $4$ -connected planar triangulation $G$ on $n$ vertices has at least $2 (n - 2) (n - 4)$ Hamiltonian cycles, with equality…

math.CO2021★ 1 cited

Number of Hamiltonian cycles in planar triangulations

Xiaonan Liu, Xingxing Yu

Whitney proved in 1931 that 4-connected planar triangulations are Hamiltonian. Hakimi, Schmeichel, and Thomassen conjectured in 1979 that if $G$ is a 4-connected planar triangulati…

math.CO2021

Hamiltonian paths and cycles in some 4-uniform hypergraphs

Guanwu Liu, Xiaonan Liu

In 1999, Katona and Kierstead conjectured that if a $k$ -uniform hypergraph $H$ on $n$ vertices has minimum co-degree $⌊ \frac{n - k + 3}{2} ⌋$ , i.e., each set of $k - 1$ …

Planar Turán Numbers of Cycles: A Counterexample

Polynomial χ-binding functions for t-broom-free graphs

Counting Hamiltonian cycles in planar triangulations

Number of Hamiltonian cycles in planar triangulations

Hamiltonian paths and cycles in some 4-uniform hypergraphs

Polynomial $χ$ -binding functions for $t$ -broom-free graphs