在1-连通和2-连通的二部图中保持连通度的一些树的研究

罗莲; 田应智

doi:10.13568/j.cnki.651094.651316.2021.03.24.0001

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在1-连通和2-连通的二部图中保持连通度的一些树的研究

更新时间：2026-01-21

- 在1-连通和2-连通的二部图中保持连通度的一些树的研究
- Journal of Xinjiang University (Natural Science Edition in Chinese and English) Vol. 39, Issue 3, Pages: 283-286(2022)
- 作者机构：
  
  新疆大学数学与系统科学学院
- 作者简介：
- 基金信息：
- DOI：10.13568/j.cnki.651094.651316.2021.03.24.0001
  CLC： O157.5
- Published：2022
- 稿件说明：
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[1]罗莲,田应智.在1-连通和2-连通的二部图中保持连通度的一些树的研究[J].新疆大学学报(自然科学版)(中英文),2022,39(03):283-286.
[1]罗莲,田应智.在1-连通和2-连通的二部图中保持连通度的一些树的研究[J].新疆大学学报(自然科学版)(中英文),2022,39(03):283-286. DOI： 10.13568/j.cnki.651094.651316.2021.03.24.0001.

DOI：10.13568/j.cnki.651094.651316.2021.03.24.0001.

摘要

在2010年

Mader猜想对任意的阶为m的树T

每一个最小度至少为■的k-连通图G中存在一个子树■

使得G-V (T′)仍然是k-连通的.对于二部图

提出了类似的猜想:对任意的二部划分为X和Y的树T (记t=max{|X|

|Y|})

每一个最小度至少为k+t的k-连通的二部图G中存在一个子树■

使得G-V (T′)仍然是k-连通的.最后验证了该猜想在k=1和k=2时

T是一个有至多3个内点的毛毛虫图的情形是对的.

Abstract

In 2010

Mader conjectured that for any tree T of order m

every k-connected graph G with minimum degree at least■ contains a subtree ■ such that G-V (T′) is still k-connected.For bipartite graphs

we proposed a similar conjecture as follows:for every positive integer k and every finite tree T with bipartition X and Y (denote t=max{|X|

|Y|})

every k-connected bipartite graph G with minimum degree at least k+t contains a subtree ■ such that G-V (T′) is still k-connected.In this paper

we confirm this conjecture for all caterpillars whose internal vertices is at most 3 when k=1 and k=2.

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references

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