Bipartite Designs

Restricted b-Factors in Bipartite Graphs and t-Designsy

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 a...

HAHA designs

The agroforestry literature makes references to HAHA designs. This paper is the first systematic study of these designs and some of their generalizations. The relationship between HAHA designs and Eulerian paths around bipartite graphs is exploited.

Some Balanced Bipartite Row-column Designs

A series of balanced bipartite row-column designs (BBPRC-designs) into sets of treatments with v1=4t+3 (test treatments) v2=2t+2 (control treatments) with varying replication has been obtained by supplementing a set of v2=2t+2 treatments in blank positions of non-orthogonal RC design of Agrawal (1966). Such designs find applications in agricultural and industrial experimentation where the inves...

Balanced bipartite 4-cycle designs

Latin Square Type Bipartite Row-column Designs

A class of Balanced Bipartite Row-Column Designs (BBPRC-designs) in two sets of treatments of sizes v1=v and v2=v+1 with replications 2(v-1) and 2v, respectively, has been constructed by replacing the ii-th positions of 2v × 2v standard cyclic latin square design in 2v treatments by 2v treatments by (2v+1)-th treatment. Such design finds applications in agricultural and industrial experimentati...

Some new constructions of imprimitive cometric association schemes

In a recent paper [9], the authors introduced the extended Q-bipartite double of an almost dual bipartite cometric association scheme. Since the association schemes arising from linked systems of symmetric designs are almost dual bipartite, this gives rise to a new infinite family of 4-class cometric schemes which are both Q-bipartite and Q-antipodal. These schemes, the schemes arising from lin...