Jiangdong Ai

collaborators

6 papers

math.CO2024

A short note on spanning even trees

Jiangdong Ai, Zhipeng Gao, Xiangzhou Liu +1

We call a tree $T$ is \emph{even} if every pair of its leaves is joined by a path of even length. Jackson and Yoshimoto~[J. Graph Theory, 2024] conjectured that every $r$ -regular n…

math.CO2024

On degree power sum in $P_{k}$ -free graphs

Jiangdong Ai, Fankang He, Yihang Liu +1

Let $G$ be a graph on $n$ vertices with degree sequence $(d_{1}, d_{2} ...... d_{n})$ . For a real $p \geq 1$ , let $D_{p} (G) = \sum_{i = 1}^{n} d_{i}^{p}$ . A Turán-type problem of degree power sum was in…

math.CO2024

Piercing independent sets in graphs without large induced matching

Jiangdong Ai, Hong Liu, Zixiang Xu +1

Given a graph $G$ , denote by $h (G)$ the smallest size of a subset of $V (G)$ which intersects every maximum independent set of $G$ . We prove that any graph $G$ without induced match…

math.CO2024

Solution on strong partition of $2$ -balanced regular multipartite tournaments

Jiangdong Ai, Fankang He, Yihang Liu

We call a partition of a $c$ -partite tournament into tournaments of order $c$ is strong if each tournament is strongly connected. The strong partition number denoted as $S T (r)$ , re…

math.CO2023

Bounds on Maximum Weight Directed Cut

Jiangdong Ai, Stefanie Gerke, Gregory Gutin +2

We obtain lower and upper bounds for the maximum weight of a directed cut in the classes of weighted digraphs and weighted acyclic digraphs as well as in some of their subclasses.…

math.CO2022

Results on the Small Quasi-Kernel Conjecture

Jiangdong Ai, Stefanie Gerke, Gregory Gutin +2

A {\em quasi-kernel} of a digraph $D$ is an independent set $Q \subseteq V (D)$ such that for every vertex $v \in V (D) \ Q$ , there exists a directed path with one or two arcs…

A short note on spanning even trees

On degree power sum in Pk​-free graphs

Piercing independent sets in graphs without large induced matching

Solution on strong partition of 2-balanced regular multipartite tournaments

Bounds on Maximum Weight Directed Cut

Results on the Small Quasi-Kernel Conjecture

On degree power sum in $P_{k}$ -free graphs

Solution on strong partition of $2$ -balanced regular multipartite tournaments