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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 $1\leq k\leq \kappa$,…

Combinatorics · Mathematics 2010-04-15 Xueliang Li , Yuefang Sun

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…

Combinatorics · Mathematics 2025-11-19 Igor Araujo , Kareem Benaissa , Richard Bi , Sean English , Shengan Wu , Pai Zheng

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…

Combinatorics · Mathematics 2012-04-12 Xueliang Li , Sujuan Liu

A path in an edge-colored graph is called a \emph{rainbow path} if all edges on it have pairwise distinct colors. For $k\geq 1$, the \emph{rainbow-$k$-connectivity} of a graph $G$, denoted $rc_k(G)$, is the minimum number of colors required…

Combinatorics · Mathematics 2012-03-06 Jing He , Hongyu Liang

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…

Combinatorics · Mathematics 2015-06-11 Allan Lo

A path in an edge-colored graph $G$, where adjacent edges may have the same color, is called a rainbow path if no two edges of the path are colored the same. The rainbow connection number $rc(G)$ of $G$ is the minimum integer $i$ for which…

Combinatorics · Mathematics 2015-03-17 Hengzhe Li , Xueliang Li , Sujuan Liu

A path in an edge-colored graph $G$ is called a rainbow path if no two edges of the path are colored the same. The minimum number of colors required to color the edges of $G$ such that every pair of vertices are connected by at least $k$…

Combinatorics · Mathematics 2012-12-27 Xiaolin Chen , Xueliang Li , Huishu Lian

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…

Combinatorics · Mathematics 2014-07-23 Qingqiong Cai , Xueliang Li , Yan Zhao

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 by $rc(G)$, is the smallest number of colors that…

Combinatorics · Mathematics 2011-10-07 Jiuying Dong , Xueliang Li

Let $k$ be a positive integer, and $G$ be a $k$-connected graph. An edge-coloured path is \emph{rainbow} if all of its edges have distinct colours. The \emph{rainbow $k$-connection number} of $G$, denoted by $rc_k(G)$, is the minimum number…

Combinatorics · Mathematics 2020-09-08 Shinya Fujita , Henry Liu , Boram Park

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…

Combinatorics · Mathematics 2012-03-15 Hengzhe Li , Xueliang Li , Yuefang Sun , Yan Zhao

We call an edge colouring of a graph G a rainbow colouring if every pair of vertices is joined by a rainbow path, i.e., a path where no two edges have the same colour. The minimum number of colours required for a rainbow colouring of the…

Combinatorics · Mathematics 2016-02-03 Annika Heckel , Oliver Riordan

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…

Combinatorics · Mathematics 2015-11-20 Wenjing Li , Xueliang Li , Di Wu

A path in an edge-colored graph $G$, where adjacent edges may have the same color, is called rainbow if no two edges of the path are colored the same. The rainbow connection number $rc(G)$ of $G$ is the smallest integer $k$ for which there…

Combinatorics · Mathematics 2011-10-14 Hengzhe Li , Xueliang Li , Yuefang Sun

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.…

Discrete Mathematics · Computer Science 2011-10-10 Prabhanjan Ananth , Meghana Nasre , Kanthi K Sarpatwar

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.…

Computational Complexity · Computer Science 2011-04-13 Prabhanjan Ananth , Meghana Nasre

A path in an edge-coloured graph is called \emph{rainbow path} if its edges receive pairwise distinct colours. An edge-coloured graph is said to be \emph{rainbow connected} if any two distinct vertices of the graph are connected by a…

Combinatorics · Mathematics 2019-11-05 Trung Duy Doan , Ingo Schiermeyer

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 it are colored the same. A nontrivial connected graph $G$ is rainbow connected if for any two vertices of $G$…

Combinatorics · Mathematics 2010-01-05 Xueliang Li , Yuefang Sun

An edge-colored graph $G$, where adjacent edges may be colored the same, is rainbow connected if any two vertices of $G$ are connected by a path whose edges have distinct colors. The rainbow connection number $rc(G)$ of a connected graph…

Combinatorics · Mathematics 2011-05-27 Xueliang Li , Sujuan Liu

An edge-colored graph $G$ is rainbow connected if every pair of vertices of $G$ are connected by a path whose edges have distinct colors. The rainbow connection number $rc(G)$ of $G$ is defined to be the minimum integer $t$ such that there…

Combinatorics · Mathematics 2012-11-06 Xueliang Li , Sujuan Liu
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