Xiaodong Xu

activity

20122022

most citedChromatic Vertex Folkman Numbers

3 citations · 4 across the 8 of their papers we have counts for

collaborators

8 papers

math.CO2022★ 1 cited

On almost perfect linear Lee codes of packing radius 2

Xiaodong Xu, Yue Zhou

More than 50 years ago, Golomb and Welch conjectured that there is no perfect Lee codes $C$ of packing radius $r$ in $Z^{n}$ for $r \geq 2$ and $n \geq 3$ . Recently, Leung an…

math.CO2021

On Some Generalized Vertex Folkman Numbers

Zohair Raza Hassan, Yu Jiang, David E. Narváez +2

For a graph $G$ and integers $a_{i} \geq 1$ , the expression $G \to (a_{1}, \dots, a_{r})^{v}$ means that for any $r$ -coloring of the vertices of $G$ there exists a monochromatic $a_{i}$ -…

math.CO2018

On a Diagonal Conjecture for Classical Ramsey Numbers

Meilian Liang, Stanisław Radziszowski, Xiaodong Xu

Let $R (k_{1}, \dots, k_{r})$ denote the classical $r$ -color Ramsey number for integers $k_{i} \geq 2$ . The Diagonal Conjecture (DC) for classical Ramsey numbers poses that if $k_1, \cdot…

math.CO2017

A Note on Upper Bounds for Some Generalized Folkman Numbers

Xiaodong Xu, Meilian Liang, Stanisław Radziszowski

We present some new constructive upper bounds based on product graphs for generalized vertex Folkman numbers. They lead to new upper bounds for some special cases of generalized ed…

math.CO2017

On the Nonexistence of Some Generalized Folkman Numbers

Xiaodong Xu, Meilian Liang, Stanisław Radziszowski

For an undirected simple graph $G$ , we write $G \to (H_{1}, H_{2})^{v}$ if and only if for every red-blue coloring of its vertices there exists a red $H_{1}$ or a blue $H_{2}$ . The g…

math.CO2016★ 3 cited

Chromatic Vertex Folkman Numbers

Xiaodong Xu, Meilian Liang, Stanisław Radziszowski

For graph $G$ and integers $a_{1} \geq \dots \geq a_{r} \geq 2$ , we write $G \to (a_{1}, \dots, a_{r})^{v}$ if and only if for every $r$ -coloring of the vertex set $V (G)$ there exists…

math.CO2015

A step forwards on the Erdős-Sós problem concerning the Ramsey numbers $R (3, k)$

Rujie Zhu, Xiaodong Xu, Stanisław Radziszowski

Let $Δ_{s} = R (K_{3}, K_{s}) - R (K_{3}, K_{s - 1})$ , where $R (G, H)$ is the Ramsey number of graphs $G$ and $H$ defined as the smallest $n$ such that any edge coloring of $K_{n}$ with two colors cont…

math.CO2012

Bounds on Shannon Capacity and Ramsey Numbers from Product of Graphs

Xiaodong Xu, Stanisław Radziszowski

In this note we study Shannon capacity of channels in the context of classical Ramsey numbers. We overview some of the results on capacity of noisy channels modelled by graphs, and…

On almost perfect linear Lee codes of packing radius 2

On Some Generalized Vertex Folkman Numbers

On a Diagonal Conjecture for Classical Ramsey Numbers

A Note on Upper Bounds for Some Generalized Folkman Numbers

On the Nonexistence of Some Generalized Folkman Numbers

Chromatic Vertex Folkman Numbers

A step forwards on the Erdős-Sós problem concerning the Ramsey numbers R(3,k)

Bounds on Shannon Capacity and Ramsey Numbers from Product of Graphs

A step forwards on the Erdős-Sós problem concerning the Ramsey numbers $R (3, k)$