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Redundant Trees in Bipartite Graphs

Author

Listed:
  • Yanmei Hong

    (School of Mathematics and Statistics, Fuzhou University, Fuzhou 350108, China
    Fujian Science & Technology Innovation Laboratory for Optoelectronic Information of China, Fuzhou 350108, China
    Key Laboratory for Operations Research and Cybernetics of Fujian Universities, Fuzhou 350108, China)

  • Yihong Wu

    (School of Mathematics and Statistics, Fuzhou University, Fuzhou 350108, China)

  • Qinghai Liu

    (Fujian Science & Technology Innovation Laboratory for Optoelectronic Information of China, Fuzhou 350108, China
    Key Laboratory for Operations Research and Cybernetics of Fujian Universities, Fuzhou 350108, China
    Center for Discrete Mathematics, Fuzhou University, Fuzhou 350108, China)

Abstract

It has been conjectured that for each positive integer k and each tree T with bipartite ( Z 1 , Z 2 ) , every k -connected bipartite graph G with δ ( G ) ≥ k + max { | Z 1 | , | Z 2 | } admits a subgraph T ′ ≅ T such that G − V ( T ′ ) is still k -connected. In this paper, we generalize the ear decompositions of 2-connected graphs into a ( k , a k ) -extensible system for a general k -connected graph. As a result, we confirm the conjecture for k ≤ 3 by proving a slightly stronger version of it.

Suggested Citation

  • Yanmei Hong & Yihong Wu & Qinghai Liu, 2025. "Redundant Trees in Bipartite Graphs," Mathematics, MDPI, vol. 13(6), pages 1-10, March.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:6:p:1005-:d:1616074
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