Exploring redundant trees in bipartite graphs

Qing Yang and Yingzhi Tian

Applied Mathematics and Computation, 2025, vol. 486, issue C

Abstract: Luo et al. conjectured that for a tree T with bipartition X and Y, if a k-connected bipartite graph G with minimum degree at least k+max⁡{|X|,|Y|}, then G has a subtree TG isomorphic to T such that G−V(TG) is k-connected. Although this conjecture has been validated for spiders and caterpillars in cases where k≤3, and also for paths with odd order, its general applicability has remained an open question. In this paper, we establish the validity of this conjecture for k≤3 with the girth under of G at least the diameter of G minus one.

Keywords: Bipartite graphs; Trees; Connectivity (search for similar items in EconPapers)
Date: 2025
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:486:y:2025:i:c:s0096300324004673

DOI: 10.1016/j.amc.2024.129006

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