Connectivity keeping stars or double-stars in 2-connected graphs.

In Mader (2010), Mader conjectured that for every positive integer k and every finite tree T with order m , every k -connected, finite graph G with δ ( G ) ≥ ⌊ 3 2 k ⌋ + m − 1 contains a subtree T ′ isomorphic to T such that G − V ( T ′ ) is k -connected. In the same paper, Mader proved that the conjecture is true when T is a path. Diwan and Tholiya (2009) verified the conjecture when k = 1 . In this paper, we will prove that Mader’s conjecture is true when T is a star or double-star and k = 2 . [ABSTRACT FROM AUTHOR]