[HTML][HTML] Total rainbow connection of digraphs

H Lei, H Liu, C Magnant, Y Shi - Discrete Applied Mathematics, 2018 - Elsevier
H Lei, H Liu, C Magnant, Y Shi
Discrete Applied Mathematics, 2018Elsevier
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 G so that any two vertices of G
are connected by a rainbow path (resp. rainbow geodesic). These two graph parameters
were introduced by Chartrand, Johns, McKeon, and Zhang in 2008. Krivelevich and Yuster
generalised this concept to the vertex-coloured setting. Similarly, Liu, Mestre, and Sousa …
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 G so that any two vertices of G are connected by a rainbow path (resp. rainbow geodesic). These two graph parameters were introduced by Chartrand, Johns, McKeon, and Zhang in 2008. Krivelevich and Yuster generalised this concept to the vertex-coloured setting. Similarly, Liu, Mestre, and Sousa introduced the version which involves total-colourings. Dorbec, Schiermeyer, Sidorowicz, and Sopena extended the concept of the rainbow connection to digraphs. In this paper, we consider the (strong) total rainbow connection number of digraphs. Results on the (strong) total rainbow connection number of biorientations of graphs, tournaments, and cactus digraphs are presented.
Elsevier
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