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

Abstract Spanning trees T 1 , T 2 , … , T k ( 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 ) | ≥ n 2 , | 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.