Redundant Trees in Bipartite Graphs

Yanmei Hong, Yihong Wu and Qinghai Liu ()
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Yanmei Hong: School of Mathematics and Statistics, Fuzhou University, 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

Mathematics, 2025, vol. 13, issue 6, 1-10

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.

Keywords: k -connected; bipartite graphs; rooted forest (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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