On the p-restricted edge connectivity of the bipartite Kneser graph H(n, k)

Title: On the p-restricted edge connectivity of the bipartite Kneser graph H(n, k)
Creator: Lin, Yuqing; Yan, Weigen; Ouyang, Zhangdong
Relation: Australasian Journal of Combinatorics Vol. 83, Issue 2, p. 265-273
Relation: https://ajc.maths.uq.edu.au/pdf/83/ajc_v83_p265.pdf
Publisher: Centre for Discrete Mathematics & Computing
Resource Type: journal article
Date: 2022
Description: Given a simple graph G, ap-restricted edge cut is a subset of edges of G whose removal disconnects G, and such that the number of vertices in each component of the resulting graph is at least p. The p-restricted edge connectivity is denoted by λp, which is the minimum cardinality over all p-restricted edge cuts. If a p-restricted edge cut (also called a λp-cut) exists, then the graph is called p-restricted edge connected, or, for short, λp-connected. Obviously, for any λp-cut F, G − F has exactly two components, and each component has at least p vertices. If the deletion of any λp-cut results in at least one component containing exactly p vertices in the resulting graph, then the graph is called super-λp.Inthispaper,we examine the p-restricted edge connectivity of the bipartite Kneser graph H(n, k) whenn ≥ 3k + 1 and show that the graph is super-λp for p ≤ 5.
Subject: p-restricted edge; graph; edge cut; Kneser graph
Identifier: http://hdl.handle.net/1959.13/1492398
Identifier: uon:53324
Identifier: ISSN:1034-4942
Language: eng

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