Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use.

A path P in an edge-colored graph (not necessarily a proper edge-coloring) is a rainbow path if no two edges of P are colored the same. For an -connected graph G and an integer k with 1 ≤ k ≤ , the rainbow k -connectivity rc k (G) of G is the minimum integer j for which there exists a j -edge-coloring of G such that every two distinct vertices of G are connected by k internally disjoint rainbow paths. The rainbow k -connectivity of the complete graph K n is studied for various pairs k , n of integers. It is shown that for every integer k ≥ 2, there exists an integer f (k ) such that rc k (K n ) = 2 for every integer n ≥ f (k ). We also investigate the rainbow k -connectivity of r -regular complete bipartite graphs for some pairs k , r of integers with 2 ≤ k ≤ r . It is shown that for each integer k ≥ 2, there exists an integer r such that rc k (K r ,r ) = 3.

No abstract

No abstract

No abstract