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Article
Peer-Review Record

k-Path-Connectivity of Completely Balanced Tripartite Graphs

by Pi Wang, Shasha Li * and Xiaoxue Gao
Reviewer 2:
Submission received: 11 May 2022 / Revised: 26 May 2022 / Accepted: 31 May 2022 / Published: 5 June 2022
(This article belongs to the Special Issue Graph Theory with Applications)

Round 1

Reviewer 1 Report

The authors consider the k-path-connectivity of complete balanced tripartite graphs.  The k-path-connectivity extends the typical notion of connectivity which is determined by the number of disjoint paths linking two vertices to the number of disjoint paths linking k vertices.  Hager conjectured a link between k-path-connectivity and connectivity, which is confirmed by the authors in this class of graphs.  The constructions are straightforward and may provide insights for more general classes of graphs, such as complete tripartite or balanced multipartite.  The paper is well written and the proofs appear to be correct.  I recommend acceptance, noting the following corrections:

Line 165: when -> When

Line 218: delete the second "and the connectivity of graphs"

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

Please see attatched report.

Comments for author File: Comments.pdf

Author Response

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Author Response File: Author Response.pdf

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