Degree sequences of connected hypergraphs and hypertrees

Boonyasombat, V.

doi:10.1007/bfb0073123

Cited by 8 publications

(3 citation statements)

References 2 publications

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“…There are several different definitions of hypertrees in the literature. Our definition of hypertrees matches the definition given by Boonyasombat in [4]. Siu [13] gave a family of definitions of hypertrees, parameterised by the amount of overlap allowed between edges.…”

Section: Introductionmentioning

confidence: 81%

The average number of spanning hypertrees in sparse uniform hypergraphs

Aldosari¹,

Greenhill²

2019

Preprint

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An r-uniform hypergraph H consists of a set of vertices V and a set of edges whose elements are r-subsets of V . We define a hypertree to be a connected hypergraph which contains no cycles. A hypertree spans a hypergraph H if it is a subhypergraph of H which contains all vertices of H. Greenhill, Isaev, Kwan and McKay (2017) gave an asymptotic formula for the average number of spanning trees in graphs with given, sparse degree sequence. We prove an analogous result for r-uniform hypergraphs with given degree sequence k = (k 1 , . . . , k n ). Our formula holds whenwhere k is the average degree and k max is the maximum degree.

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Section: Introductionmentioning

confidence: 81%

The average number of spanning hypertrees in sparse uniform hypergraphs

Aldosari¹,

Greenhill²

2019

Preprint

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“…Now suppose that s 6 and r > ρ(s), or s ∈ {2, 3, 4} and (r, s) = (2, 2). We verify the conditions of Theorem 2.1. Cooper et al [13] proved that condition (1) holds with λ j defined in (11). Condition (A2) holds by Lemma 4.4, condition (A3) holds by Lemma 4.5, and condition (A4) holds by Lemma 5.4.…”

Section: Threshold Analysismentioning

confidence: 96%

“…In fact, for n satisfying this divisibility condition, a tree is a connected hypergraph on n vertices with the smallest number of edges, exactly as in the graph case. We note also that our definition of trees in hypergraphs matches the definition given by Boonyasombat in [11], while Siu refers to the trees we consider as "traditional hypertrees" [30,Section 1.2.1].…”

Section: Introductionmentioning

confidence: 99%

Spanning trees in random regular uniform hypergraphs

Greenhill

Isaev

Liang³

2020

Preprint

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Let G n,r,s denote a uniformly random r-regular s-uniform hypergraph on the vertex set {1, 2, . . . , n}. We analyse the asymptotic distribution of Y G , the number of spanning trees in G, when r, s 2 are fixed constants, (r, s) = (2, 2), and the necessary divisibility conditions hold. Greenhill, Kwan and Wind (2014) investigated the graph case (s = 2), providing an asymptotic formula for the expected value of Y G for any fixed r 3, which was previously only known up to a constant factor. They also found the asymptotic distribution of Y G for random cubic graphs (r = 3), and made a conjecture for arbitrary r 4. Here we prove this conjecture and extend the analysis to hypergraphs. When s 5 we prove a threshold result for the property that G n,r,s contains a spanning tree. We also calculate the asymptotic distribution of Y G for all fixed integers r, s 2 such that the probability that G n,r,s has a spanning tree tends to one as n grows.

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An Efficiently Recognisable Subset of Hypergraphic Sequences

Meesum

2018

Lecture Notes in Computer Science

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Degree sequences of connected hypergraphs and hypertrees

Cited by 8 publications

References 2 publications

The average number of spanning hypertrees in sparse uniform hypergraphs

The average number of spanning hypertrees in sparse uniform hypergraphs

Spanning trees in random regular uniform hypergraphs

An Efficiently Recognisable Subset of Hypergraphic Sequences

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