<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Liu, H.</style></author><author><style face="normal" font="default" size="100%">Mestre, Â.</style></author><author><style face="normal" font="default" size="100%">Sousa, Teresa</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Rainbow vertex k-connection in graphs</style></title><secondary-title><style face="normal" font="default" size="100%">Discrete Applied Mathematics</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2013</style></year></dates><urls><related-urls><url><style face="normal" font="default" size="100%">https://docentes.fct.unl.pt/sites/default/files/tmjs/files/rvck-preprint.pdf</style></url></related-urls></urls><volume><style face="normal" font="default" size="100%">161</style></volume><pages><style face="normal" font="default" size="100%">2549-2555</style></pages><abstract><style face="normal" font="default" size="100%">&lt;p&gt;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.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">16-17</style></issue></record></records></xml>