Comments on “A Hamilton sufficient condition for completely independent spanning tree”

Spanning trees T1,T2,…,Tk (k≥2) in a graph G are called completely independent spanning trees (CISTs for short) if for any two vertices x,y of G, the paths joining x and y in these k trees are pairwise openly disjoint. Hong and Zhang (2018) recently showed that a sufficient condition for Hamiltonian...

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Bibliographic Details
Published in:Discrete Applied Mathematics 2020-09, Vol.283, p.730-733
Main Authors: Qin, Xiao-Wen, Hao, Rong-Xia, Pai, Kung-Jui, Chang, Jou-Ming
Format: Article
Language:English
Subjects:
Apexes
CIST-partition
Completely independent spanning trees
Graph theory
Sufficient condition
Trees (mathematics)
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Summary:Spanning trees T1,T2,…,Tk (k≥2) in a graph G are called completely independent spanning trees (CISTs for short) if for any two vertices x,y of G, the paths joining x and y in these k trees are pairwise openly disjoint. Hong and Zhang (2018) recently showed that a sufficient condition for Hamiltonian graphs still suffices for the existence of two CISTs. That is, if G is a graph with n vertices and |N(x)∪N(y)|≥n2, |N(x)∩N(y)|≥3 for every two nonadjacent vertices x,y of G and n≥5, then G admits two CISTs. In this note, we first attend that the restriction on the number of vertices in the statement should be revised. Moreover, we point out that there is a flaw in their proof. Accordingly, we give an amendment to correct the proof.
ISSN:0166-218X
1872-6771
DOI:10.1016/j.dam.2020.01.024