The concept of rainbow connection was introduced by Chartrand et al.[14] in 2008. It is
interesting and recently quite a lot papers have been published about it. In this survey we …

An edge-colored graph G is k-proper connected if every pair of vertices is connected by k
internally pairwise vertex-disjoint proper colored paths. The k-proper connection number of …

The concept of rainbow connection was introduced by Chartrand, Johns, McKeon and
Zhang in 2008. Nowadays it has become a new and active subject in graph theory. There is …

Let k be a positive integer and G be a k-connected graph. In 2009, Chartrand, Johns,
McKeon, and Zhang introduced the rainbow k-connection number rck (G) of G. An edge …

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 κ-connected …

Rainbow vertex-connection number is the minimum k-coloring on the vertex graph G and is
denoted by rvc (G). Besides, the rainbow-vertex connection number can be applied to some …

An edge-colouring of a graph G is rainbow k-connected if, for any two vertices of G, there are
k internally vertex-disjoint paths joining them, each of which is rainbow (ie, all edges of each …

An edge-coloured graph G is said to be rainbow-connected if any two vertices are
connected by a path whose edges have different colours. The rainbow connection number …

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 of a connected graph G, denoted …

Graph colouring is one of the best known, popular and extensively researched subject in the
field of graph theory, having a wide literature with approaches from many domains and a lot …