Colourful connection concepts in graph theory such as rainbow connection, proper connection, odd connection or conflict-free connection have received a lot of attention. For an integer \(k \ge 1\) we call a path P in a graph G k-colourful, if at least k vertices of P are pairwise differently coloured. A graph G is k-colourful connected, if any two vertices of G are connected by a k-colouful path. Now we call the least integer k, which makes G k-colourful connected, the k-colourful connection number of G. In this paper, we introduce the (strong, internal) k-colourful connection number of a graph, establish bounds for our new invariants in several graph classes as well as compute exact values for \(k\in [3]\).

图论中的多彩连接概念，例如彩虹连接，正确连接，奇数连接或无冲突连接，受到了广泛的关注。对于整数\（k \ ge 1 \），如果P的至少k个顶点成对使用不同的颜色，则我们将图G k中的路径P称为彩色的。一个图ģ是ķ，-colourful如果连接的任意两个顶点ģ通过连接ķ -colouful路径。现在我们称最小整数k，这使得G k变为彩色连接，k的连通编号为 摹。在本文中，我们介绍了一个图的（强的，内部的）k色连接数，为几个图类中的新不变量建立了边界，并计算了\（k \ in [3] \）的精确值。