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A characterization of cube-hypergraphs

Gustav Burosch, Pier Vittorio Ceccherini
1996 Discrete Mathematics  
We define the t-uniform 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.  ... 
doi:10.1016/0012-365x(94)00297-v fatcat:qgmlvstjqzcvpgkgftakny57em

(0,1)-Matrices with different rows

Hasmik Sahakyan
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 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.  ... 
doi:10.1109/csitechnol.2013.6710342 fatcat:nevptea3vfex5dg4rrusu3l2ke

Isometric embeddings into cube-hypergraphs

Gustav Burosch, Pier Vittorio Ceccherini
1995 Discrete Mathematics  
We define the t-uniform 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.  ... 
doi:10.1016/0012-365x(95)91426-q fatcat:c2o7hscz7nepbcuvtu4ym6gy4a

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.  ... 

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

H. Sahakyan
2009 Discrete Applied Mathematics  
0, 1)-matrices 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 }.  ... 
doi:10.1016/j.dam.2008.11.003 fatcat:d6jbaal23jb4znboung2bnv4n4

On the set of simple hypergraph degree sequences

Hasmik Sahakyan
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.  ... 
doi:10.12988/ams.2015.411972 fatcat:e4zjrz5nl5dcrkhqulax4yjwsm

Median graphs and Helly hypergraphs

H.M. Mulder, A. Schrijver
1979 Discrete Mathematics  
the distance function 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.  ... 
doi:10.1016/0012-365x(79)90151-1 fatcat:ox7o6icpqvd37luieolkpkygae

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.  ... 

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]

Tim Austin
2008 arXiv   pre-print
In his 1985 survey 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  ... 
arXiv:0808.2268v1 fatcat:dlskeauo75hxnepcogbyax2u74

Graphs of Acyclic Cubical Complexes

Hans-Jürgen Bandelt, Victor Chepoi
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 .  ... 
doi:10.1006/eujc.1996.0010 fatcat:n2lfnifrafbitol7u23oebhy4e

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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