2018_EJRNL_PP_PETER_DUKES_1.pdf
Terbatas Perpustakaan Prodi Arsitektur
» ITB
Terbatas Perpustakaan Prodi Arsitektur
» ITB
We introduce a generalization of group divisible designs and offer example
applications to challenging problems in design theory. The generalization considers
edge-decompositions of joins of arbitrary graphs, whereas group divisible designs
handle only joins of edgeless graphs. Our example constructions include: (1) optimal
packings with block size five for the previously unsettled congruence class v ? 13
(mod 20); (2) an optimal grooming with with ratio seven for the previously unsettled
congruence class v ? 56 (mod 84); and (3) a constructive ‘quadratic’ embedding of
partial designs with block size four.