Related papers: Inducibility of rainbow graphs
An edge-coloured graph $G$ is rainbow connected if there exists a rainbow path between any two vertices. A graph $G$ is said to be $k$-rainbow connected if there exists an edge-colouring of $G$ with at most $k$ colours that is rainbow…
A path in an edge-colored graph is said to be rainbow if no color repeats on it. An edge-colored graph is said to be rainbow $k$-connected if every pair of vertices is connected by $k$ internally disjoint rainbow paths. The rainbow…
A path in an edge-colored graph $G$, where adjacent edges may be colored the same, is called a rainbow path if no two edges of $G$ are colored the same. For a $\kappa$-connected graph $G$ and an integer $k$ with $1\leq k\leq \kappa$, the…
An edge-colored graph $G$ is $k$-color connected if, between each pair of vertices, there exists a path using at least $k$ different colors. The $k$-color connection number of $G$, denoted by $cc_{k}(G)$, is the minimum number of colors…
A path in an edge-colored graph is called {\em rainbow} if no two edges of it are colored the same. For an $\ell$-connected graph $G$ and an integer $k$ with $1\leq k\leq \ell$, the {\em rainbow $k$-connection number} $rc_k(G)$ of $G$ is…
An edge-colored graph G is rainbow connected if any two vertices are connected by a path whose edges have distinct colors. The rainbow connectivity of a connected graph G, denoted rc(G), is the smallest number of colors that are needed in…
A path in an edge-colored graph $G$, where adjacent edges may be colored the same, is a rainbow path if every two edges of it receive distinct colors. The rainbow connection number of a connected graph $G$, denoted by $rc(G)$, is the…
A path in an edge colored graph is said to be a rainbow path if no two edges on the path have the same color. An edge colored graph is (strongly) rainbow connected if there exists a (geodesic) rainbow path between every pair of vertices.…
A rainbow subgraph in an edge-coloured graph is a subgraph such that its edges have distinct colours. The minimum colour degree of a graph is the smallest number of distinct colours on the edges incident with a vertex over all vertices.…
A path in a total-colored graph is called \emph{total rainbow} if its edges and internal vertices have distinct colors. For an $\ell$-connected graph $G$ and an integer $k$ with $1\leq k \leq\ell$, the \emph{total rainbow $k$-connection…
A path in an edge-colored graph $G$, where adjacent edges may be colored the same, is called a rainbow path if no two edges of the path are colored the same. For a $\kappa$-connected graph $G$ and an integer $k$ with $1\leq k\leq \kappa$,…
An edge colored graph $G$ is rainbow edge connected if any two vertices are connected by a path whose edges have distinct colors. The rainbow connection of a connected graph $G$, denoted by $rc(G)$, is the smallest number of colors that are…
An edge-colored graph $G$ is {\em rainbow connected} if any two vertices are connected by a path whose edges have distinct colors. The {\em rainbow connection} of a connected graph $G$, denoted $rc(G)$, is the smallest number of colors that…
An edge-colored graph $G$ is rainbow connected if any two vertices are connected by a path whose edges have distinct colors. The rainbow connection number of a connected graph $G$, denoted $rc(G)$, is the smallest number of colors that are…
A path in an edge colored graph is said to be a rainbow path if no two edges on the path have the same color. An edge colored graph is (strongly) rainbow connected if there exists a (geodesic) rainbow path between every pair of vertices.…
For a given graph $H$ we define $\rho(H)$ to be the minimum order of a graph $G$ such that every proper vertex coloring of $G$ contains a rainbow induced subgraph isomorphic to $H$. We give upper and lower bounds for $\rho(H)$, compute the…
We prove that for all nonnegative integers k,s there exists c with the following property. Let G be a graph with clique number at most k and chromatic number more than c. Then for every vertex-colouring (not necessarily optimal) of G, some…
An edge-colored graph $G$, where adjacent edges may have the same color, is {\it rainbow connected} if every two vertices of $G$ are connected by a path whose edge has distinct colors. A graph $G$ is {\it $k$-rainbow connected} if one can…
An edge-coloured cycle is rainbow if the edges have distinct colours. Let $G$ be a graph such that any $k$ vertices lie in a cycle of $G$. The $k$-rainbow cycle index of $G$, denoted by $crx_k(G)$, is the minimum number of colours required…
We study the following rainbow version of subgraph containment problems in a family of (hyper)graphs, which generalizes the classical subgraph containment problems in a single host graph. For a collection $\textbf{G}=\{G_1, G_2,\ldots,…