Rainbow vertex connection of digraphs
Hui Lei, Shasha Li, Henry Liu, Yongtang Shi

TL;DR
This paper investigates the (strong) rainbow vertex-connection number in directed graphs, extending existing concepts from undirected graphs and analyzing specific classes like cycles, circulants, and tournaments.
Contribution
It introduces the study of rainbow vertex-connection in digraphs and provides results for various classes of digraphs, expanding the understanding of this graph parameter.
Findings
Results for biorientations of graphs
Analysis of cycle digraphs
Insights into circulant digraphs and tournaments
Abstract
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} if any two vertices are connected by a rainbow geodesic. The (\emph{strong}) \emph{rainbow connection number} of a connected graph is the minimum number of colours needed to make the graph (strongly) rainbow connected. These two graph parameters were introduced by Chartrand, Johns, McKeon and Zhang in 2008. As an extension, Krivelevich and Yuster proposed the concept of \emph{rainbow vertex-connection}. The topic of rainbow connection in graphs drew much attention and various similar parameters were introduced, mostly dealing with undirected graphs. Dorbec, Schiermeyer, Sidorowicz and Sopena extended the concept of the rainbow connection to digraphs.…
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Taxonomy
TopicsGraph Labeling and Dimension Problems · Advanced Graph Theory Research · Limits and Structures in Graph Theory
