Edge-Disjoint Spanning Trees, Edge Connectivity, and Eigenvalues in Graphs

2015 ◽  
Vol 81 (1) ◽  
pp. 16-29 ◽  
Author(s):  
Xiaofeng Gu ◽  
Hong-Jian Lai ◽  
Ping Li ◽  
Senmei Yao
Keyword(s):  
Spanning Trees ◽  
Edge Connectivity ◽  
Edge Disjoint

scholarly journals Edge-connectivity and edge-disjoint spanning trees

2009 ◽  
Vol 309 (5) ◽  
pp. 1033-1040 ◽  
Author(s):  
Paul A. Catlin ◽  
Hong-Jian Lai ◽  
Yehong Shao
Keyword(s):  
Spanning Trees ◽  
Edge Connectivity ◽  
Edge Disjoint

scholarly journals Anti-Ramsey Number of Edge-Disjoint Rainbow Spanning Trees

2020 ◽  
Vol 34 (4) ◽  
pp. 2346-2362
Author(s):  
Linyuan Lu ◽  
Zhiyu Wang
Keyword(s):  
Spanning Trees ◽  
Ramsey Number ◽  
Edge Disjoint

Nowhere-zero 3-flow and Z3-connectedness in graphs with four edge-disjoint spanning trees

2017 ◽  
Vol 88 (4) ◽  
pp. 577-591 ◽  
Author(s):  
Miaomiao Han ◽  
Hong-Jian Lai ◽  
Jiaao Li
Keyword(s):  
Spanning Trees ◽  
Edge Disjoint

Good orientations of unions of edge‐disjoint spanning trees

2020 ◽  
Author(s):  
Jørgen Bang‐Jensen ◽  
Stéphane Bessy ◽  
Jing Huang ◽  
Matthias Kriesell
Keyword(s):  
Spanning Trees ◽  
Edge Disjoint

scholarly journals Edge-disjoint rainbow spanning trees in complete graphs

2016 ◽  
Vol 57 ◽  
pp. 71-84 ◽  
Author(s):  
James M. Carraher ◽  
Stephen G. Hartke ◽  
Paul Horn
Keyword(s):  
Spanning Trees ◽  
Complete Graphs ◽  
Edge Disjoint

Structure Fault Tolerance of Recursive Interconnection Networks

2020 ◽  
Author(s):  
Eminjan Sabir ◽  
Jixiang Meng
Keyword(s):  
Fault Tolerance ◽  
Interconnection Networks ◽  
Theoretical Problem ◽  
Connected Subgraph ◽  
Edge Connectivity ◽  
Minimum Cardinality ◽  
Edge Disjoint ◽  
Balanced Hypercube

Abstract Motivated by effects caused by structure link faults in networks, we study the following graph theoretical problem. Let $T$ be a connected subgraph of a graph $G$ except for $K_{1}$. The $T$-structure edge-connectivity $\lambda (G;T)$ (resp. $T$-substructure edge-connectivity $\lambda ^s(G;T)$) of $G$ is the minimum cardinality of a set of edge-disjoint subgraphs $\mathcal{F}=\{T_{1},T_{2},\ldots ,T_{m}\}$ (resp. $\mathcal{F}=\{T_{1}^{^{\prime}},T_{2}^{^{\prime}},\ldots ,T_{m}^{^{\prime}}\}$) such that $T_{i}$ is isomorphic to $T$ (resp. $T_{i}^{^{\prime}}$ is a connected subgraph of $T$) for every $1 \le i \le m$, and $E(\mathcal{F})$’s removal leaves the remaining graph disconnected. In this paper, we determine both $\lambda (G;T)$ and $\lambda ^{s}(G;T)$ for $(1)$ the hypercube $Q_{n}$ and $T\in \{K_{1,1},K_{1,2},K_{1,3},P_{4},Q_{1},Q_{2},Q_{3}\}$; $(2)$ the $k$-ary $n$-cube $Q^{k}_{n}$$(k\ge 3)$ and $T\in \{K_{1,1},K_{1,2},K_{1,3},Q^{3}_{1},Q^{4}_{1}\}$; $(3)$ the balanced hypercube $BH_{n}$ and $T\in \{K_{1,1},K_{1,2},BH_{1}\}$. We also extend some known results.

Edge-disjoint spanning trees in the line graph of hypercubes

2021 ◽  
Author(s):  
Yu Qian ◽  
Baolei Cheng ◽  
Jianxi Fan ◽  
Yifeng Wang ◽  
Ruofan Jiang
Keyword(s):  
Spanning Trees ◽  
Line Graph ◽  
Edge Disjoint
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