arXiv subjects

Ying-Sian Wu

Publications and source records attributed to Ying-Sian Wu.

3 recordsLinked to original sources

arXiv2026

New results on the odd- and unique-Ramsey numbers

The odd-Ramsey number $r_{\text{odd}}(n,H)$ of a graph $H$ is the minimum number of colors needed to edge-color $K_n$ so that in every copy of $H$ some color occurs an odd number of times, and the unique-Ramsey number $r_{\text{u}}(n,H)$ is the corresponding notion in which some color is required to occur not only an odd number of times but exactly once. In this paper, we address three questions from previous papers. We show $r_{\text{odd}}(n,K_{s,t})> n^{1/\left(\frac s2+\frac 1{2\lfloor t/8 \rfloor}\right)}$ when $s\leq t$ and $s$ is odd and $t$ is even, which is log-asymptotically tight when $s$ is fixed and $t\to\infty$. Next, we consider the odd-Ramsey number when the host graph to be edge-colored is a super-Dirac graph, and show that in any host graph with minimum degree at least $n/2+2$, the odd-Ramsey number of Hamilton cycles is non-trivial. Finally, we show that $r_\text{u}(n,C_n)> n/4$, which leads to a polynomial gap between $r_\text{odd}(n,C_n)$ and $r_\text{u}(n,C_n)$.

math.CO↗

arXiv2026

Space Complexity Dichotomies for Subgraph Finding Problems in the Streaming Model

We study the space complexity of four variants of the standard subgraph finding problem in the streaming model. Specifically, given an $n$-vertex input graph and a fixed-size pattern graph, we consider two settings: undirected simple graphs, denoted by $G$ and $H$, and oriented graphs, denoted by $\vec{G}$ and $\vec{H}$. Depending on the setting, the task is to decide whether $G$ contains $H$ as a subgraph or as an induced subgraph, or whether $\vec{G}$ contains $\vec{H}$ as a subgraph or as an induced subgraph. Let Sub$(H)$, IndSub$(H)$, Sub$(\vec{H})$, and IndSub$(\vec{H})$ denote these four variants, respectively. An oriented graph is well-oriented if it admits a bipartition in which every arc is oriented from one part to the other, and a vertex is non-well-oriented if both its in-degree and out-degree are non-zero. For each variant, we obtain a complete dichotomy theorem, briefly summarized as follows. (1) Sub$(H)$ can be solved by an $\tilde{O}(1)$-pass $n^{2-Ω(1)}$-space algorithm if and only if $H$ is bipartite. (2) IndSub$(H)$ can be solved by an $\tilde{O}(1)$-pass $n^{2-Ω(1)}$-space algorithm if and only if $H \in \{P_3, P_4, co\mbox{-}P_3\}$. (3) Sub$(\vec{H})$ can be solved by a single-pass $n^{2-Ω(1)}$-space algorithm if and only if every connected component of $\vec H$ is either a well-oriented bipartite graph or a tree containing at most one non-well-oriented vertex. (4) IndSub$(\vec{H})$ can be solved by an $\tilde{O}(1)$-pass $n^{2-Ω(1)}$-space algorithm if and only if the underlying undirected simple graph $H$ is a $co\mbox{-}P_3$.

cs.DS↗

arXiv2023

Improved Lower Bounds on the Domination Number of Hypercubes and Binary Codes with Covering Radius One

A dominating set on an $n $-dimensional hypercube is equivalent to a binary covering code of length $n $ and covering radius 1. It is still an open problem to determine the domination number $γ(Q_n)$ for $ n\geq10$ and $ n\ne2^{k},2^{k}-1 $ ($k\in\mathbb{N} $). When $n$ is a multiple of 6, the best known lower bound is $γ(Q_n)\geq \frac{2^n}{n}$, given by Van Wee (1988). In this article, we present a new method using congruence properties due to Laurent Habsieger (1997) and obtain an improved lower bound $γ(Q_n)\geq \frac{(n-2)2^n }{n^2-2n-2}$ when $n$ is a multiple of 6.

math.CO↗