Abstract
An edge-coloured graph G is rainbow connected if any two vertices are connected by a path whose edges have distinct colours. The rainbow connection number of a connected graph G, denoted rc(G), is the smallest number of colours that are needed in order to make G rainbow connected. In this paper we prove that \(rc(G) < \frac{3n}{4}\) for graphs with minimum degree three, which was conjectured by Caro et al. [Y. Caro, A. Lev, Y. Roditty, Z. Tuza, and R. Yuster, On rainbow connection, The Electronic Journal of Combinatorics 15 (2008), #57.]
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References
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Schiermeyer, I. (2009). Rainbow Connection in Graphs with Minimum Degree Three. In: Fiala, J., Kratochvíl, J., Miller, M. (eds) Combinatorial Algorithms. IWOCA 2009. Lecture Notes in Computer Science, vol 5874. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10217-2_42
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DOI: https://doi.org/10.1007/978-3-642-10217-2_42
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-10216-5
Online ISBN: 978-3-642-10217-2
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