2020/12/09 by Meng Ji, Ji, Meng, Mao, Yaping
Computer Science · #Advanced Graph Theory Research #Combinatorics (math.CO) #Complexity and Algorithms in Graphs #FOS: Mathematics #Interconnection Networks and Systems
paper · pdf · doi:10.48550/arxiv.2012.04816
openalex publication_date 2020/12/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
W. Mader [J. Graph Theory 65 (2010), 61--69] conjectured that for any tree T of order m, every k-connected graph G with δ(G)≥\lfloor(3k)/(2)\rfloor+m-1 contains a tree T'≅ T such that G-V(T') remains k-connected. In 2010, Mader confirmed the conjecture for the k-connected graph if T is a path; very recently, Liu et al. confirmed the conjecture if k=2,3. The conjecture is open for k≥ 4 till now. In this paper, we show that Mader's conjecture is true for the k+1-connected graph if T is a spider and Δ(G)=|G|-1.