Chengli Li

activity

20242026

collaborators

12 papers

math.CO2026

Edge-disjoint Hamilton cycles under a bipartite-hole condition

Yanan Hu, Chengli Li, Feng Liu

In 2017, McDiarmid and Yolov introduced the bipartite-hole-number $I^\pm (G)$ and proved that $I^´ (G) \geq I^\pm (G)$ forces a Hamilton cycle. They also gave a sufficient…

math.CO2026

The number of cycles of a given length in dense hamiltonian graphs: proving Hilton's conjecture

Chengli Li, Leyou Xu, Bo Zhou

A classical theorem of Sheehan in 1977 states that every hamiltonian graph $G$ of order $n$ satisfying $e (G) > ⌊ \frac{n ^{2}}{4} ⌋ + 1$ contains at least two cycles…

math.CO2026

The maximum number of paths of a given length in a nonhamiltonian graph

Chengli Li, Xingzhi Zhan

In 1980, Paul ErdÅs posed the following problem: For every positive integer $n,$ determine a nonhamiltonian graph of order $n$ having the maximum number of Hamilton paths. We solv…

math.CO2025

Every $2$ -connected $[4, 2]$ -graph of order at least seven contains a pancyclic edge

Chengli Li, Xingzhi Zhan

A graph $G$ is called an $[s, t]$ -graph if any induced subgraph of $G$ of order $s$ has size at least $t .$ An edge $e$ in a graph $G$ of order $n$ is called pancyclic if for every i…

math.CO2025

Cycles of consecutive lengths in $3$ -connected graphs

Chengli Li, Xingzhi Zhan

Recently Lin, Wang and Zhou have proved that every $3$ -connected nonbipartite graph of minimum degree at least $k$ with $k \geq 6$ and order at least $k + 2$ contains $k$ cycles of con…

math.CO2025

Cycles and paths through vertices whose degrees are at least the bipartite-hole-number

Chengli Li, Feng Liu, Yurui Tang

The bipartite-hole-number of a graph $G$ , denoted by $I^\pm (G)$ , is the minimum integer $k$ such that there exist positive integers $s$ and $t$ with $s + t = k + 1$ , satisfy…

Edge-disjoint Hamilton cycles under a bipartite-hole condition

The number of cycles of a given length in dense hamiltonian graphs: proving Hilton's conjecture

The maximum number of paths of a given length in a nonhamiltonian graph

Every 2-connected [4,2]-graph of order at least seven contains a pancyclic edge

Cycles of consecutive lengths in 3-connected graphs

Cycles and paths through vertices whose degrees are at least the bipartite-hole-number

Every $2$ -connected $[4, 2]$ -graph of order at least seven contains a pancyclic edge

Cycles of consecutive lengths in $3$ -connected graphs