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An edge-coloured path is \emph{rainbow} if its edges have distinct colours. An edge-coloured connected graph is said to be \emph{rainbow connected} if any two vertices are connected by a rainbow path, and \emph{strongly rainbow connected}…

Combinatorics · Mathematics 2017-07-18 Hui Lei , Shasha Li , Henry Liu , Yongtang Shi

An edge (vertex) coloured graph is rainbow-connected if there is a rainbow path between any two vertices, i.e. a path all of whose edges (internal vertices) carry distinct colours. Rainbow edge (vertex) connectivity of a graph $G$ is the…

Combinatorics · Mathematics 2016-10-27 Nina Kamčev , Michael Krivelevich , Benny Sudakov

An edge-coloured path is rainbow if its edges have distinct colours. For a connected graph $G$, the rainbow connection number (resp. strong rainbow connection number) of $G$ is the minimum number of colours required to colour the edges of…

Combinatorics · Mathematics 2017-11-06 Hui Lei , Henry Liu , Colton Magnant , Yongtang Shi

An edge-colored multigraph $G$ is rainbow connected if every pair of vertices is joined by at least one rainbow path, i.e., a path where no two edges are of the same color. In the context of multilayered networks we introduce the notion of…

Combinatorics · Mathematics 2025-03-04 Josep Díaz , Öznur Yaşar Diner , Maria Serna , Oriol Serra

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 2010-11-01 Xueliang Li , Yongtang Shi

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…

Combinatorics · Mathematics 2011-10-27 Xueliang Li , Mengmeng Liu , Ingo Schiermeyer

The concept of rainbow connection was introduced by Chartrand et al. in 2008. It is fairly interesting and recently quite a lot papers have been published about it. In this survey we attempt to bring together most of the results and papers…

Combinatorics · Mathematics 2011-02-02 Xueliang Li , Yuefang Sun

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…

Combinatorics · Mathematics 2011-12-05 Arash Ahadi , Ali Dehghan

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…

Combinatorics · Mathematics 2014-12-03 Andrzej Dudek , Alan Frieze , Charalampos Tsourakakis

A path in an edge-colored graph, where adjacent edges may be colored the same, is a rainbow path if no two edges of it are colored the same. A nontrivial connected graph $G$ is rainbow connected if there is a rainbow path connecting any two…

Combinatorics · Mathematics 2010-12-24 Xueliang Li , Yuefang Sun

An edge-coloured path is rainbow if all of its edges have distinct colours. Let $G$ be a connected graph. The rainbow connection number of $G$, denoted by $rc(G)$, is the minimum number of colours in an edge-colouring of $G$ such that, any…

Combinatorics · Mathematics 2025-03-13 Rongxia Tang , Henry Liu , Yueping Shi , Chenming Wang

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…

Combinatorics · Mathematics 2008-09-16 Sourav Chakraborty , Eldar Fischer , Arie Matsliah , Raphael Yuster

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

Let $G$ be an edge-colored connected graph. A path of $G$ is called rainbow if its every edge is colored by a distinct color. $G$ is called rainbow connected if there exists a rainbow path between every two vertices of $G$. The minimum…

Combinatorics · Mathematics 2013-04-04 Jiuying Dong , Xueliang Li

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…

Computational Complexity · Computer Science 2011-11-15 Xiaolong Huang , Xueliang Li , Yongtang Shi

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

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

Let $G$ be an edge-colored graph. The color degree of a vertex $v$ of $G$, is defined as the number of colors of the edges incident to $v$. The color number of $G$ is defined as the number of colors of the edges in $G$. A rainbow triangle…

Combinatorics · Mathematics 2016-06-27 Binlong Li , Bo Ning , Chuandong Xu , Shenggui Zhang

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 rainbow (geodesic) path between every pair of vertices.…

Computational Complexity · Computer Science 2011-09-28 Shasha Li , Xueliang Li

For a graph $G$, Chartrand et al. defined the rainbow connection number $rc(G)$ and the strong rainbow connection number $src(G)$ in "G. Charand, G.L. John, K.A. Mckeon, P. Zhang, Rainbow connection in graphs, Mathematica Bohemica,…

Combinatorics · Mathematics 2010-12-15 Xiaolin Chen , Xueliang Li
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