k-path-edge-connectivity of the complete balanced bipartite graph

Yaoping Wang, Shasha Li and Zeng Zhao

Applied Mathematics and Computation, 2025, vol. 495, issue C

Abstract: Given a graph G=(V,E) and a set S⊆V(G) with |S|≥2, an S-path in G is a path that connects all vertices of S. Let ωG(S) represent the maximum number of edge-disjoint S-paths in G. The k-path-edge-connectivityωk(G) of G is then defined as min{ωG(S):S⊆V(G)and|S|=k}, where 2≤k≤|V|. Therefore, ω2(G) is precisely the edge-connectivity λ(G). In this paper, we focus on the k-path-edge-connectivity of the complete balanced bipartite graph Kn,n for all 3≤k≤2n. We show that if k=n or k=n+1, and n is odd, then ωk(Kn,n)=⌊nk2(k−1)⌋−1; otherwise, ωk(Kn,n)=⌊nk2(k−1)⌋.

Keywords: Complete balanced bipartite graphs; Path-edge-connectivity; S-paths (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:495:y:2025:i:c:s0096300325000220

DOI: 10.1016/j.amc.2025.129295

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