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A characterization of cube-hypergraphs

1996
*
Discrete Mathematics
*

We define the t-uniform

doi:10.1016/0012-365x(94)00297-v
fatcat:qgmlvstjqzcvpgkgftakny57em
*cube*-*hypergraph**of*dimension n, Q(n, t), as the*hypergraph*which is the natural analogue*of*the n-dimensional hypercube Qn' and give*a**characterization**of*those t-uniform*hypergraphs*... This extends*a*previous result*of*S. Foldes in the graph case. ... Bipartiteness will be used here to obtain*a**characterization**of**cube*-*hypergraphs*in the class*of*t-uniform connected*hypergraphs*. ...##
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(0,1)-Matrices with different rows

2013
*
Ninth International Conference on Computer Science and Information Technologies Revised Selected Papers
*

We consider (0,1)-matrices with given row and column sums, and with an additional requirement/constraintrestricted number

doi:10.1109/csitechnol.2013.6710342
fatcat:nevptea3vfex5dg4rrusu3l2ke
*of*repeated rows. ... Consider*a*family*of*sets (or*a**hypergraph*) , where , | | , is*a*finite set*of*elements, and , | | , is*a*collection*of*subsets*of*. ... Various combinatorial problems from n-*cube*geometry,*hypergraph*theory, discrete tomography problems, are effectively modeled in terms*of*(0,1) matrices. ...##
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Isometric embeddings into cube-hypergraphs

1995
*
Discrete Mathematics
*

We define the t-uniform

doi:10.1016/0012-365x(95)91426-q
fatcat:c2o7hscz7nepbcuvtu4ym6gy4a
*cube*-*hypergraphs**of*dimension n, Q(n, t), and give two*characterizations**of*those t-uniform*hypergraphs*isometrically embeddable into Q(t,n). ... This extends previous results*of*Djokovic (1973) and*of*Winkler (1984, 1985) for graphs. 0012-365X/95/$09.50 © 1995--Elsevier Science B.V. All rights reserved SSDI 0012-365X(93)E0161-V ... isometrically embeddable in*a**cube*-*hypergraph*. ...##
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Page 5185 of Mathematical Reviews Vol. , Issue 96i
[page]

1996
*
Mathematical Reviews
*

In the case D = |

*a**characterization**of*Moore*hypergraphs*is given in terms*of*diclique partitions. ... The main problem is to*characterize*the oriented*hypergraphs*(which are called Moore*hypergraphs*), on which equality in this bound is attained. ...##
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Page 791 of Mathematical Reviews Vol. , Issue 97B
[page]

1997
*
Mathematical Reviews
*

791 OSC Graph theory
97b:05123 05C75
Burosch, Gustav; Ceccherini, Pier Vittorio (l-ROME; Rome)

*A**characterization**of**cube*-*hypergraphs*. (English summary) Discrete Math. 152 (1996), no. 1-3, 55-68. ... For ¢ = 2, the*cube*-*hypergraph*Q(n, 2) is the usual n-dimensional hypercube Q,. ...##
###
Numerical characterization of n-cube subset partitioning

2009
*
Discrete Applied Mathematics
*

0, 1)-matrices

doi:10.1016/j.dam.2008.11.003
fatcat:d6jbaal23jb4znboung2bnv4n4
*Hypergraph*Tomography Partition/projection*a*b s t r*a*c t*A*general quantitative description*of*vertex subsets*of*the n-dimensional unit*cube*E n through their partitions (direct problem ...*A*complete and simple structural description*of*the numerical parameters*of*the unit*cube*partitions is presented. ... Another problem is the*characterization**of*degree sequences*of**hypergraphs*. Let H = (H(V), H(E)) be*a**hypergraph*with vertex set H(V) = {v 1 , . . . , v n }, and edge set H(E) = {E 1 , . . . , E m }. ...##
###
On the set of simple hypergraph degree sequences

2015
*
Applied Mathematical Sciences
*

*A*structural

*characterization*

*of*the lowest and highest rank maximal elements

*of*̂( ) was provided in an earlier study. ... For

*a*given , 0 < ≤ 2 , let ( ) denote the set

*of*all

*hypergraphic*sequences for

*hypergraphs*with vertices and hyperedges. ... Section 2 determines

*a*

*characterization*

*of*the lowest rank. We obtain

*a*series

*of*minimal elements

*of*̂( ) and prove that these elements are the lowest rank non-

*hypergraphic*sequences. ...

##
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Median graphs and Helly hypergraphs

1979
*
Discrete Mathematics
*

the distance function

doi:10.1016/0012-365x(79)90151-1
fatcat:ox7o6icpqvd37luieolkpkygae
*of*the graph). ... One-to-one correspondences are establish~d between the following combinatorial structures: (i) median interval structures (or median segments, introduced by SHOLANDER); (ii) maximal Helly*hypergraphs*such ... also*characterized*medians). 3. 3 - 2 . 32 MEDIAN GRAPHS AND MAXIMAL HELLY COPAIR*HYPERGRAPHS*. ...##
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Page 3818 of Mathematical Reviews Vol. , Issue 2002F
[page]

2002
*
Mathematical Reviews
*

The authors give several

*characterizations**of*graphs whose as- sociated neighborhood*hypergraphs*have the Helly property, in- cluding Theorem: Let G be*a*connected graph such that any chain induced by ...*A**hypergraph**of**a*finite set S is*a*finite family (£;)*of*nonempty subsets*of*S (called hyperedges) with |) E; = S. ...##
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Page 8780 of Mathematical Reviews Vol. , Issue 99m
[page]

1999
*
Mathematical Reviews
*

*A*. (3-WTRL-C; Waterloo, ON)

*A*

*characterization*

*of*signed

*hypergraphs*and its applications to VLSI via minimization and logic synthesis. (English summary) Discrete Appl. ... In particular,

*a*structural

*characterization*

*of*balanced signed

*hypergraphs*is given, and two optimization problems related to the balance property—the maximum balance and the minimum covering problems—are ...

##
###
Page 850 of Mathematical Reviews Vol. 47, Issue 4
[page]

1974
*
Mathematical Reviews
*

jie M) is

*a**hypergraph*such that |Z;*a*E,|= ry. ... That is, given any graph G that is the dual*of**a*planar 4-connected graph, there is*a*sequence*of*duals*of*planar 4-connected graphs Gy, G,, ---, G, such that G, is the graph*of*the*cube*, G,,=G, and each ...##
###
Page 4220 of Mathematical Reviews Vol. , Issue 80K
[page]

1980
*
Mathematical Reviews
*

n-

*cube*such that with any three vertices*of*G their median in the n-*cube*is also*a*vertex*of*G”. ...*A*3-uniform*hypergraph*consists*of**a*vertex set X together with*a*collection*of*triples*of*X called edges. Suppose one k-colors the n vertices*of**a*3-uniform*hypergraph*, using all k colors. ...##
###
On the geometry of a class of invariant measures and a problem of Aldous
[article]

2008
*
arXiv
*
pre-print

In his 1985 survey

arXiv:0808.2268v1
fatcat:dlskeauo75hxnepcogbyax2u74
*of*notions*of*exchangeability, Aldous introduced*a*form*of*exchangeability corresponding to the symmetries*of*the infinite discrete*cube*, and asked whether these exchangeable probability ... simplex (that is, its subset*of*extreme points is closed), in the case*of**cube*-exchangeability it is*a*copy*of*the Poulsen simplex (in which the extreme points are dense). ... The form*of*previous representation theorems for exchangeable measures In this section we introduce*a*general template for*a*kind*of*representation theorem for exchangeable laws, which in particular*characterizes*...##
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Graphs of Acyclic Cubical Complexes

1996
*
European journal of combinatorics (Print)
*

*A*C Y C L I C C U B I C

*A*L C O M P L E X E S The notion

*of*acyclicity is borrowed from the theory

*of*data base schemes alias

*hypergraphs*. ... Vertices

*of*

*a*cubical complex are 0-dimensional

*cubes*

*of*. In the ( underlying ) graph G

*of*the complex two vertices

*of*are adjacent if they constitute

*a*1-dimensional

*cube*. ... The research

*of*the second author , who is on leave from the Universitatea de stat din Moldova , Chis ¸ ina

*â*u , was supported by the Alexander von Humboldt Stiftung . ...

##
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Page 3265 of Mathematical Reviews Vol. 58, Issue 5
[page]

1979
*
Mathematical Reviews
*

We give

*a**characterization**of*all partitive*hypergraphs*as well as*of*those which are associated with graphs or hyper- graphs. ... Authors’ summary: “We define*a*new class*of**hypergraphs*(parti- tive*hypergraphs*) which generalize both the set*of*all externally telated subsets*of**a*graph and the set*of*all committees*of**a**hypergraph*...
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