Highly connected triples and Mader's conjecture

Abstract

AbstractMader proved that, for any tree of order , every ‐connected graph with contains a subtree such that is ‐connected. We proved that any graph with minimum degree contains ‐connected triples. As a corollary, we prove that, for any tree of order , every ‐connected graph with contains a subtree such that is still ‐connected, improving Mader's condition to a linear bound.