Yanbo Zhang

activity

20182026

most citedProof of a Conjecture on Online Ramsey Numbers of Paths

2 citations · 3 across the 10 of their papers we have counts for

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9 papers · 1 filter

math.CO2026

Ramsey numbers and Gallai--Ramsey numbers of disjoint unions of cherries

Yanbo Zhang, Qian Chen, Yaojun Chen

For graphs $G_{1}, \dots, G_{k}$ , the Ramsey number $R (G_{1}, \dots, G_{k})$ is the smallest positive integer $N$ such that every $k$ -edge-coloring of $K_{N}$ contains a monochromatic copy of…

math.CO2026

New bounds for Ramsey numbers involving graphs with a center

Yanbo Zhang, Yaojun Chen

Let $F_{n}$ , $W_{n}$ , and $K_{n}$ be the graphs obtained by joining a vertex to $n$ independent edges, a cycle and a path of order $n - 1$ , respectively. In this paper, we give n…

math.CO2024

Disproofs of four Gallai-Ramsey-type conjectures

Yanbo Zhang, Yaojun Chen

As a significant variation of Ramsey numbers, the Gallai-Ramsey number $G R_{k} (H)$ refers to the smallest positive integer $r$ such that, by coloring the edges of $K_{r}$ with at most…

math.CO2024

Size Ramsey numbers of small graphs versus fans or paths

Yufan Li, Yanbo Zhang, Yunqing Zhang

For two graphs $G_{1}$ and $G_{2}$ , the size Ramsey number $r^(G_{1}, G_{2})$ is the smallest positive integer $m$ for which there exists a graph $G$ of size $m$ such that for any red-…

math.CO2024

Matching-star size Ramsey numbers under connectivity constraint

Fanghua Guo, Yanbo Zhang, Yunqing Zhang

Recently, Caro, Patkós, and Tuza (2022) introduced the concept of connected Turán number. We study a similar parameter in Ramsey theory. Given two graphs $G_{1}$ and $G_{2}$ , the size…

math.CO2023

Ramsey goodness of fans

Yanbo Zhang, Yaojun Chen

Given two graphs $G_{1}$ and $G_{2}$ , the Ramsey number $r (G_{1}, G_{2})$ refers to the smallest positive integer $N$ such that any graph $G$ with $N$ vertices contains $G_{1}$ as a subgraph,…

math.CO2023★ 2 cited

Proof of a Conjecture on Online Ramsey Numbers of Paths

Yanbo Zhang, Yixin Zhang

For two graphs $G_{1}$ and $G_{2}$ , the online Ramsey number $r ~ (G_{1}, G_{2})$ is the smallest number of edges that Builder draws on an infinite empty graph to guarantee that there…

math.CO2023

Proof of a Conjecture on Online Ramsey Numbers of Stars versus Paths

Ruyu Song, Sha Wang, Yanbo Zhang

Given two graphs $G$ and $H$ , the online Ramsey number $r ~ (G, H)$ is defined to be the minimum number of rounds that Builder can always guarantee a win in the following $(G,…

math.CO2020★ 1 cited

The Ramsey number of a long even cycle versus a star

Peter Allen, Tomasz Łuczak, Joanna Polcyn +1

We find the exact value of the Ramsey number $R (C_{2 ℓ}, K_{1, n})$ , when $ℓ$ and $n = O (ℓ^{10/9})$ are large. Our result is closely related to the behaviour of Turán number $e…