scholarly journals On homeomorphically irreducible spanning trees in cubic graphs

2018 ◽  
Vol 89 (2) ◽  
pp. 93-100 ◽  
Author(s):  
Arthur Hoffmann-Ostenhof ◽  
Kenta Noguchi ◽  
Kenta Ozeki
Keyword(s):  
Spanning Trees ◽  
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.

scholarly journals Spanning trees with many leaves in cubic graphs

1989 ◽  
Vol 13 (6) ◽  
pp. 669-695 ◽  
Author(s):  
Jerrold R. Griggs ◽  
Daniel J. Kleitman ◽  
Aditya Shastri
Keyword(s):  
Spanning Trees ◽  
Cubic Graphs

scholarly journals A 5/3-Approximation for Finding Spanning Trees with Many Leaves in Cubic Graphs

2008 ◽  
pp. 184-192 ◽  
Author(s):  
José R. Correa ◽  
Cristina G. Fernandes ◽  
Martín Matamala ◽  
Yoshiko Wakabayashi
Keyword(s):  
Spanning Trees ◽  
Cubic Graphs

scholarly journals Reflexive coloring complexes for 3-edge-colorings of cubic graphs

2021 ◽  
Vol 344 (4) ◽  
pp. 112309
Author(s):  
Fiachra Knox ◽  
Bojan Mohar ◽  
Nathan Singer
Keyword(s):  
Cubic Graphs ◽  
Edge Colorings
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