Jia Zhou

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20242026

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15 papers · 1 filter

math.CO2026

Paths with Prescribed Endpoints in Semicomplete and Locally Semicomplete Digraphs

Hanzhi Bai, Jin Yan, Jia Zhou

We study two open path problems with prescribed endpoints posed by Bang-Jensen and Gutin. The first asks for a longest $(x, y)$ -path in a semicomplete digraph. The second asks wheth…

math.CO2026

Ramsey--Turán Factors of Non-directed Oriented Cycles in Oriented Graphs

Jia Zhou, Yunshu Gao

Let $C$ be any orientation of the cycle $C_{ℓ}$ which is not directed. We prove that, for every integer $ℓ \geq 3$ and every $μ > 0$ , there is a real $γ$ such tha…

math.CO2026

Dominant-Degree Conditions for Ramsey--Turán Factors of Non-Directed Cycle Orientations

Jia Zhou, Yunshu Gao

Let $\Cvec$ be a fixed orientation of the cycle $C_{ℓ}$ , $ℓ \geq 3$ , which is not directed. For an oriented graph $D$ , let $d_{D}^{*} (v) := max {d_{D}^{+} (v), d_{D}^{-} (v)},$ and let \[ \sigor…

math.CO2026

A Chvátal--Erdős type condition for supereulerian digraphs with $α_{2} = 4$

Zirui Liu, Jin Yan, Jia Zhou

A digraph is \textbf{supereulerian} if it contains a spanning closed trail. Let $α_{2} (D)$ denote the maximum cardinality of a vertex set inducing no 2-cycle. In this paper, we chara…

math.CO2026

Complexity of Arc-Decompositions involving Perfect Matchings and Cycle Factors

Hangning Liu, Jørgen Bang-Jensen, Jin Yan +1

For two digraph properties $P_{1}$ and $P_{2}$ , a $(P_{1}, P_{2})$ -arc-decomposition of a digraph $D$ is a partition $A (D) = A_{1} \cup ˙ A_{2}$ such that the spanning subdigraphs $D[A_…

math.CO2026

Sparse spanning $k$ -strong oriented subdigraphs in split digraphs

Jia Zhou, Jørgen Bang-Jensen, Jin Yan

Jackson and Thomassen conjectured that every $2 k$ -strong digraph admits a spanning $k$ -strong oriented subdigraph [Ann. N. Y. Acad. Sci. 555 (1989) 402-412]. The conjecture holds f…

math.CO2026

Highly connected spanning oriented subdigraphs in generalizations of semicomplete digraphs

Jia Zhou, Jørgen Bang-Jensen, Tong Zhou +1

Let $k$ be a positive integer. Jackson and Thomassen conjectured in 1989 that there exists an integer function $f (k)$ such that every $f (k)$ -strong digraph admits a spanning $k$ -st…

math.CO2026

K-Arc-Strong Orientations Of Semicomplete Digraphs

Tong Zhou, Jørgen Bang-Jensen, Jia Zhou +1

Results by Jackson and Frank imply that every 2k-arc-strong digraph D contains a spanning k-arc-strong oriented subdigraph. This is best possible, even for very dense digraphs. A d…

math.CO2026

On the 2-Linkage Problem for Split Digraphs

Xiaoying Chen, Jørgen Bang-Jensen, Jin Yan +1

A digraph is {\bf $ k $-linked} if for arbitary two disjoint vertex sets $\{s_1, \ldots, s_k\}$ and $\{t_1, \ldots, t_k\}$, there exist vertex-disjoint directed paths \(P_1,…

math.CO2025

Proof of the linkage conjecture for highly connected tournaments

Jia Zhou, Jin Yan

A digraph $D$ is $k$ -linked if for every $2 k$ distinct vertices $x_{1}, \dots, x_{k}, y_{1}, \dots, y_{k}$ in $D$ , there exist $k$ pairwise vertex-disjoint paths $P_{1}, \dots, P_{k}$ such…

math.CO2025

On the $k$ -linkage problem for generalizations of semicomplete digraphs

Jia Zhou, Jørgen Bang-Jensen, Jin Yan

A directed graph (digraph) $D$ is $k$ -linked if $∣ D ∣ \geq 2 k$ , and for any $2 k$ distinct vertices $x_{1}, \dots, x_{k}, y_{1}, \dots, y_{k}$ of $D$ , there exist vertex-disjoi…

math.CO2024

Solutions to the linkage conjecture in tournaments

Jia Zhou, Jin Yan

A digraph $D$ is $k$ -linked if for every $2 k$ -tuple $x_{1}, \dots, x_{k}, y_{1}, \dots, y_{k}$ of distinct vertices in $D$ , there exist $k$ pairwise vertex-disjoint paths $P_1,\ldots,…

math.CO2024

Semi-Degree Condition for Arbitrary $H$ -Linked Oriented Graphs

Jia Zhou, Jin Yan

Let $H$ be a multi-digraph on $h$ vertices with $q$ arcs. An \textbf{ $H$ -subdivision} in a digraph $D$ is a subdigraph obtained by replacing every arc $uv$ of $H$ with a path…

math.CO2024

Bipartitions with prescribed order of highly connected digraphs

Yuzhen Qi, Jin Yan, Jia Zhou

A digraph is strongly connected if it has a directed path from $x$ to $y$ for every ordered pair of distinct vertices $x, y$ and it is strongly $k$ -connected if it has at least $k+…

math.CO2024

The generalizations of Hamiltonian in oriented graphs

Jia Zhou, Zhilan Wang, Jin Yan

An oriented graph is an orientation of a simple graph. In 2009, Keevash, Kühn and Osthus proved that every sufficiently large oriented graph $D$ of order $n$ with $(3 n - 4) /8$ is Ham…

Paths with Prescribed Endpoints in Semicomplete and Locally Semicomplete Digraphs

Ramsey--Turán Factors of Non-directed Oriented Cycles in Oriented Graphs

Dominant-Degree Conditions for Ramsey--Turán Factors of Non-Directed Cycle Orientations

A Chvátal--Erdős type condition for supereulerian digraphs with α2​=4

Complexity of Arc-Decompositions involving Perfect Matchings and Cycle Factors

Sparse spanning k-strong oriented subdigraphs in split digraphs

Highly connected spanning oriented subdigraphs in generalizations of semicomplete digraphs

K-Arc-Strong Orientations Of Semicomplete Digraphs

On the 2-Linkage Problem for Split Digraphs

Proof of the linkage conjecture for highly connected tournaments

On the k-linkage problem for generalizations of semicomplete digraphs

Solutions to the linkage conjecture in tournaments

Semi-Degree Condition for Arbitrary H-Linked Oriented Graphs

Bipartitions with prescribed order of highly connected digraphs

The generalizations of Hamiltonian in oriented graphs

A Chvátal--Erdős type condition for supereulerian digraphs with $α_{2} = 4$

Sparse spanning $k$ -strong oriented subdigraphs in split digraphs

On the $k$ -linkage problem for generalizations of semicomplete digraphs

Semi-Degree Condition for Arbitrary $H$ -Linked Oriented Graphs