Exploring redundant trees in bipartite graphs

IF 4.3 3区材料科学 Q1 ENGINEERING, ELECTRICAL & ELECTRONIC

ACS Applied Electronic Materials Pub Date : 2024-08-27 DOI:10.1016/j.amc.2024.129006

Qing Yang, Yingzhi Tian

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引用次数: 0

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 $T_{G}$ isomorphic to T such that $G - V (T_{G})$ is k-connected. Although this conjecture has been validated for spiders and caterpillars in cases where $k \leq 3$ , 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 $k \leq 3$ with the girth under of G at least the diameter of G minus one.

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探索双向图中的冗余树

Luo 等人猜想，对于具有双分区 X 和 Y 的树 T，如果一个 k 连接的双分区图 G 的最小度至少为 k+max{|X||,|Y||}，那么 G 有一个与 T 同构的子树 TG，这样 G-V(TG)就是 k 连接的。虽然这一猜想已经在 k≤3 的情况下对蜘蛛和毛毛虫以及奇数阶路径进行了验证，但其普遍适用性仍是一个未决问题。在本文中，我们将证明这一猜想在 k≤3 且 G 的周长至少为 G 的直径减一的情况下的有效性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

ACS Applied Electronic Materials Multiple-

CiteScore

7.20

自引率

4.30%

发文量

567