Tao Feng

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5 papers · 1 filter

math.CO2026

Even cycle decomposition thresholds for dense multipartite graphs

Weiyi Sun, Tao Feng, Shikang Yu

Let $r \geq 2$ be an integer. An $r$ -partite graph $Γ$ with vertex partition $V_{1}, \dots, V_{r}$ is $2$ -balanced if there exists a positive integer $n$ such that $n \leq ∣ V_{i} ∣ \leq 2 n$ f…

math.CO2026

Finite groups with quadratic splitting fields for all Cayley graphs

Majid Arezoomand, Alireza Abdollahi, Tao Feng +1

For a graph $Γ$ , the splitting field of $Γ$ is defined as the splitting field of the characteristic polynomial of $Γ$ over rationals. The algebraic degree of $Γ$ is defined by the…

math.CO2026

On the completion of $ε$ -dense partial Latin squares

Shikang Yu, Tao Feng

A partial Latin square of order $n$ is called $ε$ -dense if each row and each column contains at most $ε n$ filled cells, and each symbol occurs at most $ε n$ times. A partial Latin s…

math.CO2026

Fractional clique decompositions of dense balanced multipartite graphs

Tao Feng, Hengrui Liu, Shikang Yu

This paper concerns fractional $K_{s}$ -decompositions of multipartite graphs. For integers $r \geq s \geq 3$ , we consider balanced $r$ -partite graphs $G$ on $r n$ vertices. We establish n…

math.CO2024

On $2$ -integral Cayley graphs

Alireza Abdollahi, Majid Arezoomand, Tao Feng +1

In this paper, we introduce the concept of $k$ -integral graphs. A graph $Γ$ is called $k$ -integral if the extension degree of the splitting field of the characteristic polynomial o…

Even cycle decomposition thresholds for dense multipartite graphs

Finite groups with quadratic splitting fields for all Cayley graphs

On the completion of ε-dense partial Latin squares

Fractional clique decompositions of dense balanced multipartite graphs

On 2-integral Cayley graphs

On the completion of $ε$ -dense partial Latin squares

On $2$ -integral Cayley graphs