@article {3731,
	title = {Total rainbow k-connection in graphs},
	journal = {Discrete Applied Mathematics},
	volume = {174},
	year = {2014},
	pages = {92-101},
	abstract = {<p>Let k be a positive integer and G be a k-connected graph. In 2009, Chartrand, Johns, McKeon, and Zhang introduced the rainbow k-connection number rc_k(G) of G. An edge-coloured path is rainbow if its edges have distinct colours. Then, 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) has since been studied by numerous researchers. An analogue of the function rc_k(G) involving vertex colourings, the rainbow vertex k-connection number rvc_k(G), was subsequently introduced. In this paper, we introduce a version which involves total colourings. A total-coloured path is total-rainbow if its edges and internal vertices have distinct colours. The total rainbow k-connection number of G, denoted by trc_k(G), is the minimum number of colours required to colour the edges and vertices of $G$, so that any two vertices of $G$ are connected by $k$ internally vertex-disjoint total-rainbow paths. We study the function trc_k(G) when G is a cycle, a wheel, and a complete multipartite graph. We also compare the functions rc_k(G), rvc_k(G), and trc_k(G), by considering how close and how far apart trc_k(G) can be from rc_k(G) and rvc_k(G).</p>
},
	attachments = {https://docentes.fct.unl.pt/sites/default/files/tmjs/files/trc-preprint.pdf},
	author = {Liu, H. and Mestre, {\^A}. and Sousa, Teresa}
}
