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Rainbow Connectivity of Cacti and of Some Infinite Digraphs

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Alva-Samos J., Montellano-Ballesteros J. J.

Discussiones Mathematicae Graph Theory

2017

tom 37

nr 2

301-313

An arc-coloured digraph D = (V,A) is said to be rainbow connected if for every pair {u, v} ⊆ V there is a directed uv-path all whose arcs have different colours and a directed vu-path all whose arcs have different colours. The minimum number of colours required to make the digraph D rainbow connected is called the rainbow connection number of D, denoted rc⃗ (D). A cactus is a digraph where each arc belongs to exactly one directed cycle. In this paper we give sharp upper and lower bounds for the rainbow connection number of a cactus and characterize those cacti whose rainbow connection number is equal to any of those bounds. Also, we calculate the rainbow con- nection numbers of some infinite digraphs and graphs, and present, for each n ≥ 6, a tournament of order n and rainbow connection number equal to 2.

Ograniczanie wyników

1 Discussiones Mathematicae Graph Theory

1 Alva-Samos J.

1 Montellano-Ballesteros J. J.

1 2017

Wyniki wyszukiwania

Rainbow Connectivity of Cacti and of Some Infinite Digraphs