arXiv subjects

Yunshu Gao

Publications and source records attributed to Yunshu Gao.

4 recordsLinked to original sources

arXiv2026

Antidirected forests in digraphs

A digraph is antidirected if every vertex has indegree zero or outdegree zero. Let $k\ge2$, and let $F$ be an antidirected forest with $k$ arcs and no isolated vertices. We prove that every digraph $D$ of order $n$ with more than $g_k(n):=2\max\left\{\binom{2k-1}{2}, (k-1)\left(n-\frac{k}{2}\right)\right\}$ arcs contains $F$ as a subdigraph. For $n\ge2k-1$, this threshold equals $2\mathrm{ex}(n,kK_2)$ and is attained by symmetric digraphs arising from extremal $kK_2$-free graphs. Consequently, the maximum directed extremal number over all such forests is $2\mathrm{ex}(n,kK_2)$. The proof combines a counting inequality for rooted antidirected forests, embeddings extending vertex-disjoint arcs, and vertex deletion. In the remaining case, the Gallai--Edmonds decomposition of the underlying graph gives the required bound on the number of arcs.

math.CO↗

arXiv2026

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

Let $\overrightarrow{C}$ be any orientation of the cycle $C_{\ell}$ which is not directed. We prove that, for every integer $\ell\ge3$ and every $μ>0$, there is a real $γ$ such that every sufficiently large oriented graph $D$ with $\ell\mid |D|$, minimum semidegree at least $(1/4+μ)|D|$ and independence number at most $γ|D|$ has a $\overrightarrow{C}$-factor. The constant $1/4$ is asymptotically tight. This proof establishes Ramsey-Turán type lattice absorption lemmas and an almost covering theorem via the oriented tree embedding lemma under chromatic number constraints.

math.CO↗

arXiv2026

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

Let $\Cvec$ be a fixed orientation of the cycle $C_\ell$, $\ell\ge3$, which is not directed. For an oriented graph $D$, let $d_D^*(v):=\max\{d_D^+(v),d_D^-(v)\},$ and let \[ \sigore(D):=\min\bigl\{d_D^*(x)+d_D^*(y):x\ne y,\ xy,yx\notin A(D)\bigr\}, \] with $\sigore(D)=\infty$ if the underlying graph of $D$ is complete. We prove that, for every $μ>0$, there exist $γ>0$ and $n_0$ such that every $n\ge n_0$ with $\ell\mid n$ and every $n$-vertex oriented graph $D$ satisfying \[ α(D)\leγn \text{ and } {\sigore(D)\ge\left(\frac34+μ\right)n} \] contains a $\Cvec$-factor. {Additionally, for every fixed $s\ge2$ and every fixed real constant $C$, we construct arbitrarily large oriented graphs with $\sigore(D)\ge \frac34n+C$ that contain no $C_{2s}^{\ad}$-factor. More precisely, $C:=\frac34α(D)-2$ for $s=2$ and $C:=\frac14α(D)-\frac32$ for $s\ge3$.} This paper develops a weighted reduction framework adapted to dominant degree condition, proves the absorption lemma via closed-cluster merging with even-walk, and derives almost-perfect tiling structures by virtue of Farkas-lemma-based fractional decomposition.

math.CO↗

arXiv2022

Degradation-invariant Enhancement of Fundus Images via Pyramid Constraint Network

As an economical and efficient fundus imaging modality, retinal fundus images have been widely adopted in clinical fundus examination. Unfortunately, fundus images often suffer from quality degradation caused by imaging interferences, leading to misdiagnosis. Despite impressive enhancement performances that state-of-the-art methods have achieved, challenges remain in clinical scenarios. For boosting the clinical deployment of fundus image enhancement, this paper proposes the pyramid constraint to develop a degradation-invariant enhancement network (PCE-Net), which mitigates the demand for clinical data and stably enhances unknown data. Firstly, high-quality images are randomly degraded to form sequences of low-quality ones sharing the same content (SeqLCs). Then individual low-quality images are decomposed to Laplacian pyramid features (LPF) as the multi-level input for the enhancement. Subsequently, a feature pyramid constraint (FPC) for the sequence is introduced to enforce the PCE-Net to learn a degradation-invariant model. Extensive experiments have been conducted under the evaluation metrics of enhancement and segmentation. The effectiveness of the PCE-Net was demonstrated in comparison with state-of-the-art methods and the ablation study. The source code of this study is publicly available at https://github.com/HeverLaw/PCENet-Image-Enhancement.

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