相关论文: A note on Gallai-Ramsey number of even wheels

A Gallai coloring is a coloring of the edges of a complete graph without rainbow triangles, and a Gallai $k$-coloring is a Gallai coloring that uses $k$ colors. Given an integer $k\ge1$ and graphs $H_1, \ldots, H_k$, the Gallai-Ramsey…

A Gallai coloring is a coloring of the edges of a complete graph without rainbow triangles, and a Gallai $k$-coloring is a Gallai coloring that uses at most $k$ colors. Given an integer $k\ge1$ and graphs $H_1, \ldots, H_k$, the…

A Gallai coloring is a coloring of the edges of a complete graph without rainbow triangles, and a Gallai $k$-coloring is a Gallai coloring that uses at most $k$ colors. For an integer $k\geq 1$, the Gallai-Ramsey number $GR_k(H)$ of a given…

A Gallai coloring is a coloring of the edges of a complete graph without rainbow triangles, and a Gallai $k$-coloring is a Gallai coloring that uses $k$ colors. We study Ramsey-type problems in Gallai colorings. Given an integer $k\ge1$ and…

A Gallai $k$-coloring is a $k$-edge coloring of a complete graph in which there are no rainbow triangles. For two given graphs $H, G$ and two positive integers $k,s$ with that $s\leq k$, the $k$-colored Gallai-Ramsey number $gr_{k}(K_{3}:…

For a graph $H$ and an integer $k\ge1$, the $k$-color Ramsey number $R_k(H)$ is the least integer $N$ such that every $k$-coloring of the edges of the complete graph $K_N$ contains a monochromatic copy of $H$. Let $C_m$ denote the cycle on…

A Gallai coloring of a complete graph is an edge-coloring such that no triangle has all its edges colored differently. A Gallai $k$-coloring is a Gallai coloring that uses $k$ colors. Given an integer $k\ge1$ and a graph $H$, the…

A colored complete graph is said to be Gallai-colored if it contains no rainbow triangle. This property has been shown to be equivalent to the existence of a partition of the vertices (of every induced subgraph) in which at most two colors…

A Gallai $k$-coloring is a $k$-edge coloring of a complete graph in which there are no rainbow triangles. For given graphs $G_1, G_2, G_3$ and nonnegative integers $r, s, t$ with that $k=r+s+t$, the $k$-colored Gallai-Ramsey number…

Given two graphs $G$ and $H$, the $k$-colored Gallai-Ramsey number $gr_k(G : H)$ is defined to be the minimum integer $n$ such that every $k$-coloring of the complete graph on $n$ vertices contains either a rainbow copy of $G$ or a…

A Gallai-coloring (Gallai-$k$-coloring) is an edge-coloring (with colors from $\{1, 2, \ldots, k\}$) of a complete graph without rainbow triangles. Given a graph $H$ and a positive integer $k$, the $k$-colored Gallai-Ramsey number $GR_k(H)$…

Given a graph $H$ and an integer $k\ge1$, the Gallai-Ramsey number $GR_k(H)$ is defined to be the minimum integer $n$ such that every $k$-edge coloring of $K_n$ contains either a rainbow (all different colored) triangle or a monochromatic…

Given two graphs $G$ and $H$ and a positive integer $k$, the $k$-color Gallai-Ramsey number, denoted by $gr_{k}(G : H)$, is the minimum integer $N$ such that for all $n \geq N$, every $k$-coloring of the edges of $K_{n}$ contains either a…

Given graphs $G$ and $H$ and a positive integer $k$, the Gallai-Ramsey number $gr_{k}(G : H)$ is the minimum integer $N$ such that for any integer $n \geq N$, every $k$-edge-coloring of $K_{n}$ contains either a rainbow copy of $G$ or a…

Given a nonempty graph $G$, a collection of nonempty graphs $\cal{H}$, and a positive integer $k$, the Gallai-Ramsey number $\mathrm{gr}_k(G:\mathcal{H})$ is defined to be the minimum positive integer $n$ such that every exact…

Given two non-empty graphs $G,H$ and a positive integer $k$, the Gallai-Ramsey number $\operatorname{gr}_k(G:H)$ is defined as the minimum integer $N$ such that for all $n\geq N$, every $k$-edge-coloring of $K_n$ contains either a rainbow…

Given a graph $H$ and an integer $k\ge1$, the Gallai-Ramsey number $GR_k(H)$ is defined to be the minimum integer $n$ such that every $k$-edge coloring of the complete graph $K_n$ contains either a rainbow (all different colored) triangle…

Given a graph $G$ and a positive integer $k$, define the \emph{Gallai-Ramsey number} to be the minimum number of vertices $n$ such that any $k$-edge coloring of $K_n$ contains either a rainbow (all different colored) triangle or a…

We study Ramsey-type problems in Gallai-colorings. Given a graph $G$ and an integer $k\ge1$, the Gallai-Ramsey number $gr_k(K_3,G)$ is the least positive integer $n$ such that every $k$-coloring of the edges of the complete graph on $n$…

A Gallai coloring of a complete graph $K_n$ is an edge coloring without triangles colored with three different colors. A sequence $e_1\ge \dots \ge e_k$ of positive integers is an $(n,k)$-sequence if $\sum_{i=1}^k e_i=\binom{n}{2}$. An…