Fragments in kcritical n-connected graphs

Madar conjectured that every k-critical n-connected non-complete graph G has (2k + 2) pairwise disjoint fragments. We show that Mader's conjecture holds if the order of G is greater than (k + 2)n. From this, it implies that two other conjectures on k-critical n-connected graphs posed by Entringer, Slater, and Mader also hold if the cardinality of the graphs is large. © 1995 John Wiley & Sons, Inc.