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Exploring redundant trees in bipartite graphs

Author

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  • Yang, Qing
  • Tian, Yingzhi

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.

Suggested Citation

  • Yang, Qing & Tian, Yingzhi, 2025. "Exploring redundant trees in bipartite graphs," Applied Mathematics and Computation, Elsevier, vol. 486(C).
    • Handle: RePEc:eee:apmaco:v:486:y:2025:i:c:s0096300324004673
    DOI: 10.1016/j.amc.2024.129006
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