Monochromatic [formula omitted]-connection of graphs.

An edge-coloured path is monochromatic if all of its edges have the same colour. For a k -connected graph G , the monochromatic k -connection number of G , denoted by m c k (G) , is the maximum number of colours in an edge-colouring of G such that, any two vertices are connected by k internally vertex-disjoint monochromatic paths. In this paper, we shall study the parameter m c k (G). We obtain bounds for m c k (G) , for general graphs G. We also compute m c k (G) exactly when k is small, and G is a graph on n vertices, with a spanning k -connected subgraph having the minimum possible number of edges, namely ⌈ k n 2 ⌉. We prove a similar result when G is a bipartite graph. [ABSTRACT FROM AUTHOR]