scholarly journals Max-leaves spanning tree is APX-hard for cubic graphs

2012 ◽  
Vol 12 ◽  
pp. 14-23 ◽  
Author(s):  
Paul Bonsma
Keyword(s):  
Spanning Tree ◽  
Cubic Graphs

scholarly journals Spanning trees in random regular uniform hypergraphs

2021 ◽  
pp. 1-25
Author(s):  
Catherine Greenhill ◽  
Mikhail Isaev ◽  
Gary Liang
Keyword(s):  
Asymptotic Distribution ◽  
Spanning Tree ◽  
Spanning Trees ◽  
Threshold Value ◽  
Regular Graphs ◽  
Cubic Graphs ◽  
Trivial Case ◽  
Uniform Hypergraphs ◽  
Vertex Set ◽  
Number Of Spanning Trees

Abstract Let $${{\mathcal G}_{n,r,s}}$$ denote a uniformly random r-regular s-uniform hypergraph on the vertex set {1, 2, … , n}. We establish a threshold result for the existence of a spanning tree in $${{\mathcal G}_{n,r,s}}$$ , restricting to n satisfying the necessary divisibility conditions. Specifically, we show that when s ≥ 5, there is a positive constant ρ(s) such that for any r ≥ 2, the probability that $${{\mathcal G}_{n,r,s}}$$ contains a spanning tree tends to 1 if r > ρ(s), and otherwise this probability tends to zero. The threshold value ρ(s) grows exponentially with s. As $${{\mathcal G}_{n,r,s}}$$ is connected with probability that tends to 1, this implies that when r ≤ ρ(s), most r-regular s-uniform hypergraphs are connected but have no spanning tree. When s = 3, 4 we prove that $${{\mathcal G}_{n,r,s}}$$ contains a spanning tree with probability that tends to 1, for any r ≥ 2. Our proof also provides the asymptotic distribution of the number of spanning trees in $${{\mathcal G}_{n,r,s}}$$ for all fixed integers r, s ≥ 2. Previously, this asymptotic distribution was only known in the trivial case of 2-regular graphs, or for cubic graphs.

Bipolar Neutrosophic Cubic Graphs and Its Applications

2020 ◽  
pp. 492-536
Author(s):  
C. Antony Crispin Sweety ◽  
K. Vaiyomathi ◽  
F. Nirmala Irudayam
Keyword(s):  
Real Time ◽  
Spanning Tree ◽  
Minimum Spanning Tree ◽  
Cartesian Product ◽  
Score Function ◽  
Cubic Graphs ◽  
Cubic Graph ◽  
Tree Algorithm ◽  
Algebraic Properties ◽  
Real Time Application

The authors introduce neutrosophic cubic graphs and single-valued netrosophic Cubic graphs in bipolar setting and discuss some of their algebraic properties such as Cartesian product, composition, m-union, n-union, m-join, n-join. They also present a real time application of the defined model which depicts the main advantage of the same. Finally, the authors define a score function and present minimum spanning tree algorithm of an undirected bipolar single valued neutrosophic cubic graph with a numerical example.

Self-Protected Spanning Tree Based Recovery Scheme to Protect against Single Failure

2009 ◽  
Vol E92-B (3) ◽  
pp. 909-921
Author(s):  
Depeng JIN ◽  
Wentao CHEN ◽  
Li SU ◽  
Yong LI ◽  
Lieguang ZENG
Keyword(s):  
Spanning Tree ◽  
Recovery Scheme
Sign in / Sign up

Export Citation Format

Share Document