Related papers: On Neutral Edge Sets in Anti-Ramsey Numbers

According to a study by Erd\H{o}s et al. in 1975, the anti-Ramsey number of a graph \(G\), denoted as \(AR(n, G)\), is defined as the maximum number of colors that can be used in an edge-coloring of the complete graph \(K_n\) without…

The anti-Ramsey number $ar(G,H)$ with input graph $G$ and pattern graph $H$, is the maximum positive integer $k$ such that there exists an edge coloring of $G$ using $k$ colors, in which there are no rainbow subgraphs isomorphic to $H$ in…

A subgraph of an edge-colored graph is rainbow if all of its edges have different colors. Let $G$ and $H$ be two graphs. The anti-Ramsey number $\ar(G, H)$ is the maximum number of colors of an edge-coloring of $G$ that does not contain a…

An edge-colored graph is called \textit{rainbow graph} if all the colors on its edges are distinct. Given a positive integer $n$ and a graph $G$, the \textit{anti-Ramsey number} $ar(n,G)$ is defined to be the minimum number of colors $r$…

An edge-colored graph is called rainbow if all the colors on its edges are distinct. Given a positive integer n and a graph G, the anti-Ramsey number ar(n,G) is the maximum number of colors in an edge-coloring of K_{n} with no rainbow copy…

A subgraph of an edge-colored graph is rainbow, if all of its edges have different colors. For a graph $G$ and a family $\mathcal{H}$ of graphs, the anti-Ramsey number $ar(G, \mathcal{H})$ is the maximum number $k$ such that there exists an…

The anti-Ramsey number $AR(n,G$), for a graph $G$ and an integer $n\geq|V(G)|$, is defined to be the minimal integer $r$ such that in any edge-colouring of $K_n$ by at least $r$ colours there is a multicoloured copy of $G$, namely, a copy…

A subgraph in an edge-colored graph is called rainbow if all its edges have distinct colors. For a graph $G$ and an integer $n$, the anti-Ramsey number $AR(n,G)$ is the maximum number of colors in an edge-coloring of $K_n$ that contains no…

We call a subgraph of an edge-colored graph rainbow subgraph, if all of its edges have different colors. The anti-Ramsey number of a graph $G$ in a complete graph $K_{n}$, denoted by $ar(K_{n}, G)$, is the maximum number of colors in an…

An edge-colored graph $G$ is called \textit{rainbow} if every edge of $G$ receives a different color. Given any host graph $G$, the \textit{anti-Ramsey} number of $t$ edge-disjoint rainbow spanning trees in $G$, denoted by $r(G,t)$, is…

The anti-Ramsey number, $AR(n,G)$, for a graph $G$ and an integer $n\geq|V(G)|$, is defined to be the minimal integer $r$ such that in any edge-colouring of $K_n$ by at least $r$ colours there is a multicoloured copy of $G$, namely, a copy…

An edge-colored graph is called \textit{rainbow graph} if all the colors on its edges are distinct. For a given positive integer $n$ and a family of graphs $\mathcal{G}$, the anti-Ramsey number $ar(n, \mathcal{G})$ is the smallest number of…

An edge-colored graph $G$ is called rainbow if every edge of $G$ receives a different color. The anti-Ramsey number of $t$ edge-disjoint rainbow spanning trees, denoted by $r(n,t)$, is defined as the maximum number of colors in an…

The anti-Ramsey numbers are a fundamental notion in graph theory, introduced in 1978, by Erd\" os, Simonovits and S\' os. For given graphs $G$ and $H$ the \emph{anti-Ramsey number} $\textrm{ar}(G,H)$ is defined to be the maximum number $k$…

The anti-Ramsey number $Ar(G,H)$ is the maximum number of colors in an edge-coloring of $G$ with no rainbow copy of $H$. In this paper, we determine the exact anti-Ramsey number in the generalized Petersen graph $P_{n,k}$ for cycles $C_d$,…

An edge-colored graph is called a rainbow graph if all its edges have distinct colors. The anti-Ramsey number $ar(n, G)$, for a graph $G$ and a positive integer $n$, is defined as the minimum number of colors $r$ such that every exact…

The anti-Ramsey number, $ar(G, H)$ is the minimum integer $k$ such that in any edge colouring of $G$ with $k$ colours there is a rainbow subgraph isomorphic to $H$, i.e., a copy of $H$ with each of its edges assigned a different colour. The…

For a given graph $H$, the anti-Ramsey number of $H$ is the maximum number of colors in an edge-coloring of a complete graph which does not contain a rainbow copy of $H$. In this paper, we extend the decomposition family of graphs to the…

Let $n, r, s$ be three positive integers such that $n\geq 2s+5$. Let $K_r$ denote the complete graph of order $r$. Given a graph $F$, the anti-Ramsey number $ar(n,F)$ is defined as the minimum number $C$ such that any edge-coloring of $K_n$…

For a fixed graph $F$, the $\textit{anti-Ramsey number}$, $AR(n,F)$, is the maximum number of colors in an edge-coloring of $K_n$ which does not contain a rainbow copy of $F$. In this paper, we determine the exact value of anti-Ramsey…