A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is `application/pdf`

.

## Filters

##
###
The number of connected sparsely edged uniform hypergraphs

1997
*
Discrete Mathematics
*

Certain families

doi:10.1016/s0012-365x(96)00076-3
fatcat:dydcuzj5dvgm3dr72exuq3uena
*of*d-*uniform**hypergraphs*are counted. In particular,*the**number**of**connected*d-*uniform**hypergraphs*with r vertices and r + k hyperedges, where k = o(log r/log tog r), is found. ... A*hypergraph*H is a pair (V,E) , where*the*set*of*hyperedges E is*the*family*of*subset*of**the*vertex set V. A sequence*of*voelvl ...ekvk, where v; are vertices*of*H, ... [6] ,*the*structure*of*a 'typical'*connected*graphs with n vertices and n + k*edges*has also been examined. Much less is known about*the**number**of**hypergraphs**of*a prescribed size. ...##
###
Sparse Hypergraphs and Pebble Game Algorithms
[article]

2007
*
arXiv
*
pre-print

We extend several well-known theorems

arXiv:math/0703921v1
fatcat:iwctiihw6rhxxmhzta7ansb46e
*of*Haas, Lovász, Nash-Williams, Tutte, and White and Whiteley, linking arboricity*of*graphs to certain counts on*the**number**of**edges*. ... We also address*the*problem*of*finding lower-dimensional representations*of**sparse**hypergraphs*, and identify a critical behaviour in terms*of**the*sparsity parameters k and ℓ. ...*The*out-degree*of*a vertex is*the**number**of**edges*which identify it as*the*tail and*connect*v to V − v;*the*in-degree is*the**number**of**edges*that do not identify it as*the*tail. ...##
###
Sparse hypergraphs and pebble game algorithms

2009
*
European journal of combinatorics (Print)
*

We extend several well-known theorems

doi:10.1016/j.ejc.2008.12.018
fatcat:h53pzoivcfdndoosb2rguplnnq
*of*Haas, Lovász, Nash-Williams, Tutte, and White and Whiteley, linking arboricity*of*graphs to certain counts on*the**number**of**edges*. ... We also address*the*problem*of*finding lower-dimensional representations*of**sparse**hypergraphs*, and identify a critical behavior in terms*of**the*sparsity parameters k and . ...*The*out-degree*of*a vertex is*the**number**of**edges*which identify it as*the*tail and*connect*v to V − v;*the*in-degree is*the**number**of**edges*that do not identify it as*the*tail. ...##
###
Toric algebra of hypergraphs
[article]

2013
*
arXiv
*
pre-print

*The*

*edges*

*of*any

*hypergraph*parametrize a monomial algebra called

*the*

*edge*subring

*of*

*the*

*hypergraph*. ... We study presentation ideals

*of*these

*edge*subrings, and describe their generators in terms

*of*balanced walks on

*hypergraphs*. ... Acknowledgements

*The*authors thank György Turán for inspiring discussions, at

*the*start

*of*this project, about

*the*fundamental problem

*of*walks in

*hypergraphs*; and also Elizabeth Gross for suggesting

*the*...

##
###
Asymptotic growth of sparse saturated structures is locally determined

1992
*
Discrete Mathematics
*

., Asymptotic growth

doi:10.1016/0012-365x(92)90692-9
fatcat:7jws22nhpbbcjl3hh4ouhfkfbq
*of**sparse*saturated structures is locally determined, Discrete Mathematics 108 (1992) 397-402. ...*The*'dual'*of*Twain's problem Let 9 and X be r-*uniform**hypergraphs*without multiple*edges*, and denote by #(9 < X)*the**number**of*subhypergraphs isomorphic to 9 in X. ... We introduce some new*hypergraph*invariants, called local density and local*sparseness**of*a*hypergraph*.F and prove that their values completely determine*the*order*of*magnitude*of**the*smallest*number*...##
###
Toric algebra of hypergraphs

2013
*
Journal of Algebraic Combinatorics
*

*The*

*edges*

*of*any

*hypergraph*parametrize a monomial algebra called

*the*

*edge*subring

*of*

*the*

*hypergraph*. ... We study presentation ideals

*of*these

*edge*subrings, and describe their generators in terms

*of*balanced walks on

*hypergraphs*. ... Acknowledgements

*The*authors thank György Turán for inspiring discussions, at

*the*start

*of*this project, about

*the*fundamental problem

*of*walks in

*hypergraphs*; and also Elizabeth Gross for suggesting

*the*...

##
###
Page 6541 of Mathematical Reviews Vol. , Issue 93m
[page]

1993
*
Mathematical Reviews
*

An r-

*uniform**hypergraph*/ is strongly ¥ -saturated if for every r-element set C not in # (that is, C is an*edge**of**the*comple- ment*of*# with respect to*the*complete r-*uniform**hypergraph*)*the**number**of*... .¥) and ssat(n,.F ) denote*the*minimum*number**of**edges*in a weakly 7 - saturated and a strongly ¥-saturated r-*uniform**hypergraph*on n vertices, respectively. ...##
###
A Sparse Model of Quantum Holography
[article]

2020
*
arXiv
*
pre-print

*The*resulting model has a new parameter, k, defined as

*the*ratio

*of*

*the*

*number*

*of*terms in

*the*Hamiltonian to

*the*

*number*

*of*degrees

*of*freedom, with

*the*

*sparse*limit corresponding to

*the*thermodynamic ... We study a

*sparse*version

*of*

*the*Sachdev-Ye-Kitaev (SYK) model defined on random

*hypergraphs*constructed either by a random pruning procedure or by randomly sampling regular

*hypergraphs*. ... In a d-regular, q-

*uniform*

*hypergraph*,

*the*total

*number*

*of*terms is dN/q, so we set d = kq to keep

*the*

*number*

*of*total terms equal to kN . ...

##
###
Natural realizations of sparsity matroids

2011
*
Ars Mathematica Contemporanea
*

structure

doi:10.26493/1855-3974.197.461
fatcat:k5idpgif3jde7al6w22mnz6f7a
*of**the*underlying*hypergraph*G. ... Motivated by problems in rigidity theory, we give a new linear representation theorem for*the*(k, )-*sparse**hypergraphs*that is natural; i.e.,*the*representing matrix captures*the*vertex-*edge*incidence ... A*hypergraph*G is defined to be d-*uniform*if all*the**edges*have d endpoints. ...##
###
Natural realizations of sparsity matroids
[article]

2010
*
arXiv
*
pre-print

structure

arXiv:0711.3013v5
fatcat:ne3zthmvhzh4ngajxjvmjhe7m4
*of**the*underlying*hypergraph*G. ... Motivated by problems in rigidity theory, we give a new linear representation theorem for*the*(k,l)-*sparse**hypergraphs*that is natural; i.e.,*the*representing matrix captures*the*vertex-*edge*incidence ... In Section 4, we describe two extensions*of*Theorem A: to non-*uniform*(k, ℓ)-*sparse**hypergraphs*and to (k, ℓ)-graded-*sparse**hypergraphs*. ...##
###
Probabilistic analysis of strong hypergraph coloring algorithms and the strong chromatic number

1987
*
Discrete Mathematics
*

In these spaces

doi:10.1016/0012-365x(87)90101-4
fatcat:utsx5xodindb3bt4zq62sjofay
*the**number**of*colors used by our algorithms is almost surely within a small constant factor (less than 4)*of**the*strong chromatic*number**of**the**hypergraph*. 0012-365X/87/$3.50 © 198"/, Elsevier ... We present coloring algorithms for several strong coloring problems and analyze their performance in spaces*of*random*hypergraphs*. ... Acknowledgment I would like to thank Eli Shamir for many discussions on*the*subject. ...##
###
Higher order interactions destroy phase transitions in Deffuant opinion dynamics model
[article]

2021
*
arXiv
*
pre-print

We show that including higher order interactions induces a drastic change in

arXiv:2111.12165v1
fatcat:pocaqut35vhejgsvu4o33xbbhu
*the*onset*of*consensus for random*hypergraphs*; instead*of**the*sharp phase transition, characteristic*of**the*dyadic Deffuant ...*The*generalized model is naturally encoded in a*hypergraph*. We study this dynamics in different*hypergraph*topologies, from random*hypergraph*ensembles, to spatially embedded hyper-lattices. ... ACKNOWLEDGMENTS*The*authors acknowledge*the*OpLaDyn grant obtained in*the*4th round*of**the*Trans-Atlantic Platform Digging into Data Challenge (2016-147 ANR OPLADYN TAP-DD2016) and Labex MME-DII (Grant ...##
###
Consistency of spectral hypergraph partitioning under planted partition model

2017
*
Annals of Statistics
*

*Hypergraph*partitioning lies at

*the*heart

*of*a

*number*

*of*problems in machine learning and network sciences. ... In this paper, we present a planted partition model for

*sparse*random non-

*uniform*

*hypergraphs*that generalizes

*the*stochastic block model. ...

*The*model generates a sequence

*of*planted

*sparse*

*uniform*

*hypergraphs*, which taken together, represent

*the*random

*hypergraph*. ...

##
###
Coloring sparse hypergraphs
[article]

2014
*
arXiv
*
pre-print

Fix k ≥ 3, and let G be a k-

arXiv:1404.2895v1
fatcat:5ngshikawrewxjvlmlppojnrmu
*uniform**hypergraph*with maximum degree Δ. Suppose that for each l = 2, ..., k-1, every set*of*l vertices*of*G is in at most Δ^(k-l)/(k-1)/f*edges*. ... Then*the*chromatic*number**of*G is O( (Δ/ f)^1/(k-1)). This extends results*of*Frieze and*the*second author and Bennett and Bohman. ...*The*degree*of*a vertex u ∈ V (G) is*the**number**of**edges*containing that vertex.*The*maximum degree*of*a*hypergraph*G is*the*maximum degree*of*a vertex v ∈ V (G). ...##
###
Zero-One Law for random uniform hypergraphs
[article]

2016
*
arXiv
*
pre-print

In this work limit probabilities

arXiv:1607.07654v1
fatcat:d56xwmitjzatrlmndmnbwxlc2i
*of*first-order properties*of**the*random s-*uniform**hypergraph*in*the*binomial model G^s(n,p) are studied. ... Moreover, for any rational ρ≥ 1/(s-1) we prove*the*existence*of*a strictly balanced s-*uniform**hypergraph*with*the*density ρ. ... An s-*uniform**hypergraph*, or s-*hypergraph*, G is a pair (V (G), E(G)) consisting*of*two sets,*the*vertices V (G) and*edges*E(G)*of*G, where each*edge*e ∈ E(G) is a set*of*s elements*of*V (G). ...
« Previous

*Showing results 1 — 15 out of 2,329 results*