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On various (strong) rainbow connection numbers of graphs. (arXiv:1601.01063v3 [math.CO] UPDATED)
来源于:arXiv
An edge-coloured path is \emph{rainbow} if all the edges have distinct
colours. For a connected graph $G$, the \emph{rainbow connection number}
$rc(G)$ is the minimum number of colours in an edge-colouring of $G$ such that,
any two vertices are connected by a rainbow path. Similarly, the \emph{strong
rainbow connection number} $src(G)$ is the minimum number of colours in an
edge-colouring of $G$ such that, any two vertices are connected by a rainbow
geodesic (i.e., a path of shortest length). These two concepts of connectivity
in graphs were introduced by Chartrand et al.~in 2008. Subsequently,
vertex-coloured versions of both parameters, $rvc(G)$ and $srvc(G)$, and a
total-coloured version of the rainbow connection number, $trc(G)$, were
introduced. In this paper we introduce the strong total rainbow connection
number $strc(G)$, which is the version of the strong rainbow connection number
using total-colourings. Among our results, we will determine the strong total
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