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### Bipartite Designs [chapter]

Grigor Gasparyan
1998 Lecture Notes in Computer Science
We show how the results relate to design theory, and then apply the results to derive sharper characterizations of ( ; !)-graphs.  ...  If for each i n, both Pni and P=i are f0; 1g-polyhedra then P has at most two fractional vertices, both of which are (r; s)-design vertices. us call the pair of matrices (A; B) a (bipartite) d-design if  ...  In this paper we would like to investigate the d-designs a bit more generally. Our main goal is to nd su cient conditions which force a d-design to become an (r; s)-design.  ...

### Resolvable balanced bipartite designs

Charlotte Huang
1976 Discrete Mathematics
A balanced bipartite design, BBB(u, kl, k2, A), is an arrangement of v elements into b bio&s, each containing k elements such that each element OCCURS in exactly F blocks and any two distinct elements  ...  A resolvable baianced bipartite design, RBBD(u, k 1, k2, A), is a BBID(u, kl , k2, A), the b blocks of which can be divided into r sets which are called complete replications, such that ach complete replication  ...  , we are concerned with a design which is a BBD with an extra condition imposed on it.  ...

### Balanced bipartite weighing designs

Charlotte Huang
1976 Journal of combinatorial theory. Series A
A balanced bipartite weighing design, (briefly BBWD (v, k, , k, , &)) is an arrangement of ~1 elements into b blocks, each containing k elements, such that each element occurs in exactly P blocks, any  ...  Some general methods for constructing BBWD's as well as a table of all designs with v Q 13 are obtained. Ail rights of reproduction in any form reserved.  ...  Several classes of CD's have been studied, for example, balanced Y-designs (e.g., [S] ), balanced circuit designs and balanced bipartite designs (e.g., [97) where the graph G is a path, a circuit and  ...

### Non-regular square bipartite designs

Caterina De Simone, Grigor Gasparyan, Paolo Nobili
2002 Linear Algebra and its Applications
A (d, λ) bipartite design with m = n is called a (d, λ) square bipartite design (SBD).  ...  A (d, λ) bipartite design with m = n + 1 is called an extremal bipartite design; pairs (A, B) of matrices that define extremal bipartite designs are studied in  .  ...  If A and B have no one-columns, then (A, B) is a square bipartite design. Obviously, every regular square bipartite design is a λ-pair. In general, not every square bipartite design is a λ-pair.  ...

### Balanced bipartite 4-cycle designs

Hung-Lin Fu
2005 The Australasian Journal of Combinatorics

### Causal Inference with Bipartite Designs [article]

Nick Doudchenko, Minzhengxiong Zhang, Evgeni Drynkin, Edoardo Airoldi, Vahab Mirrokni, Jean Pouget-Abadie
2020 arXiv   pre-print
We evaluate these methods using a bipartite graph from a publicly available dataset studied in previous work on bipartite experiments, showing through simulations a significant bias reduction and improved  ...  These experiments are particularly useful in settings where strong interference effects occur between units of a bipartite graph.  ...  In this paper, we study the estimation of causal effects in a bipartite design setting.  ...

### Neighbor-Balanced Bipartite Block Designs

N. R. Abeynayake, Seema Jaggi, Cini Varghese
2011 Communications in Statistics - Theory and Methods
A block design with neighbor effects for two disjoint sets of treatments is said to be neighbor-balanced bipartite block (NBBPB) design if every test treatment from first set has every other test treatment  ...  Under the block design set-up with b blocks of size k each, following is the model for analyzing a design for test treatments-control treatments comparison with neighbor effects: Y = 1 + + 1 + 2 + D +  ...

### Bipartite Biregular Cages and Block Designs [article]

Gabriela Araujo-Pardo, Alejandra Ramos-Rivera, Robert Jajcay
2019 arXiv   pre-print
An (n,m;g)-bipartite biregular cage is a bipartite biregular (n,m;g)-graph of minimum order.  ...  A bipartite biregular (n,m;g)-graph G is a bipartite graph of even girth g having the degree set {n,m} and satisfying the additional property that the vertices in the same partite set have the same degree  ...  The number of blocks is denoted by b and the design is denoted as a (v, k, λ)design. Theorem 2.  ...

### Designing a strategic bipartite matching market

Rahul Jain
2007 2007 46th IEEE Conference on Decision and Control
CONCLUSIONS AND FURTHER WORK We posed the problem of bipartite matching with strategic players.  ...  Note that the mechanism is strongly budget-balanced by design µ i = λ j if x * ij = 1.  ...

### Bipartite graphs with five eigenvalues and pseudo designs

Ebrahim Ghorbani
2011 Journal of Algebraic Combinatorics
A pseudo (v, k, )-design is a pair (X, B) where X is a v-set and B={B_1,...  ...  Marrero on characterization of pseudo (v, k, )-designs are obtained.  ...  The author is grateful to Osvaldo Marrero for supplying the literature of pseudo designs, to Jack Koolen for carefully reading the manuscript, and to the referees whose helpful comments improved the presentation  ...

### Restrictedb-factors in bipartite graphs andt-designs

Ivette Arámbula, Illya V. Hicks
2006 Journal of combinatorial designs (Print)
We present a new equivalence result between restricted b-factors in bipartite graphs and combinatorial t-designs. This result is useful in the construction of t-designs by polyhedral methods.  ...  We propose a novel linear integer programming formulation, which we call GDP, for the problem of finding t-designs that has a noteworthy advantage compared to the traditional set-covering formulation.  ...  We contribute by showing that the problem of finding a combinatorial t-design is equivalent to the problem of finding a biclique-free b-factor in a complete bipartite graph.  ...

### Constructions of partially balanced bipartite block designs

Sanpei Kageyama, Kishore Sinha
1991 Discrete Mathematics
Constructions of partially balanced bipartite block designs, Discrete Mathematics 92 (1991) 137-144.  ...  Methods of construction of group divisible partially balanced bipartite bkxk designs are presented.  ...  In general, the construction problem on GD PBB designs may be more complicated than that of balanced bipartite block designs.  ...

### Design and Analysis of Bipartite Experiments under a Linear Exposure-Response Model [article]

Christopher Harshaw, Fredrik Sävje, David Eisenstat, Vahab Mirrokni, Jean Pouget-Abadie
2021 arXiv   pre-print
In addition, we introduce a cluster-based design, Exposure-Design, that uses heuristics to increase the precision of the ERL estimator by realizing a desirable exposure distribution.  ...  The two sets of units are connected by a bipartite graph, governing how the treated units can affect the outcome units.  ...  The exposure distribution depends on the underlying bipartite graph and the experimental design, both of which are known to the experimenter.  ...

### Congruences modulo 9 for bipartitions with designated summands

Robert Xiaojian HAO, Erin Yiying SHEN
2018 Turkish Journal of Mathematics
For instance, π = (2 ′ , 2 ′ ) is a bipartition of 4 with designated summands. Let P D −2 (n) denote the number of bipartitions of n with designated summands.  ...  More specifically, a bipartition with designated summands is a bipartition π = (π 1 , π 2 ) for which π 1 and π 2 are both partitions with designated summands.  ...

### Mono-multi bipartite Ramsey numbers, designs, and matrices

Paul N. Balister, András Gyárfás, Jenoő Lehel, Richard H. Schelp
2006 Journal of combinatorial theory. Series A
Our general bound uses Füredi's result on fractional matchings of uniform hypergraphs and we show that it is sharp if certain block designs exist.  ...  Eroh and Oellermann defined BRR(G 1 , G 2 ) as the smallest N such that any edge coloring of the complete bipartite graph K N,N contains either a monochromatic G 1 or a multicolored G 2 .  ...  Brouwer for the discussion concerning his 3-(17, 8, 14) design.  ...
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