@article {3732,
	title = {Rainbow vertex k-connection in graphs},
	journal = {Discrete Applied Mathematics},
	volume = {161},
	year = {2013},
	pages = {2549-2555},
	abstract = {<p>Let k be a positive integer and G be a k-connected graph. An edge-coloured path is rainbow if its edges have distinct colours. The rainbow k-connection number of G, denoted by rc_k(G), is the minimum number of colours required to colour the edges of G so that any two vertices of G are connected by k internally vertex-disjoint rainbow paths. The function rc_k(G) was first introduced by Chartrand, Johns, McKeon, and Zhang in 2009, and has since attracted considerable interest. In this paper, we consider a version of the function rc_k(G) which involves vertex-colourings. A vertex-coloured path is vertex-rainbow if its internal vertices have distinct colours. The rainbow vertex k-connection number of G, denoted by rvc_k(G), is the minimum number of colours required to colour the vertices of G so that any two vertices of G are connected by k internally vertex-disjoint vertex-rainbow paths. We shall study the function rvc_k(G) when G is a cycle, a wheel, and a complete multipartite graph. We also construct graphs G where rc_k(G) is much larger than rvc_k(G) and vice versa so that we cannot in general bound one of rc_k(G) and rvc_k(G) in terms of the other.</p>
},
	attachments = {https://docentes.fct.unl.pt/sites/default/files/tmjs/files/rvck-preprint.pdf},
	author = {Liu, H. and Mestre, {\^A}. and Sousa, Teresa}
}
