1 citations · 1 across the 7 of their papers we have counts for
11 papers
Group divisible designs with block size five: direct constructions
Anthony D. Forbes
We give direct constructions for 233 group divisible designs with block size five, mostly of type , .
Group divisible designs with block size five
Anthony D. Forbes
We report some group divisible designs with block size five, including types and . As a consequence we are able to extend the known spectrum for 5-GDDs of type $g…
Generalized pentagonal geometries
Anthony D. Forbes, Carrie G. Rutherford
A pentagonal geometry PENT(, ) is a partial linear space, where every line is incident with points, every point is incident with lines, and for each point , there…
Pentagonal geometries with block sizes 3, 4 and 5
Anthony D. Forbes
A pentagonal geometry PENT(, ) is a partial linear space, where every line, or block, is incident with points, every point is incident with lines, and for each point…
Existence results for pentagonal geometries
Anthony D. Forbes, Terry S. Griggs, Klara Stokes
New results on pentagonal geometries PENT(k,r) with block sizes k = 3 or k = 4 are given. In particular we completely determine the existence spectra for PENT(3,r) systems with the…
Designs for graphs with six vertices and ten edges -- II
Anthony D. Forbes, Terry S. Griggs
The design spectrum has been determined for ten of the 15 graphs with six vertices and ten edges. In this paper we solve the design spectrum problem for the remaining five graphs w…
Group divisible designs with block size four and type
Anthony D. Forbes
We discuss group divisible designs with block size four and type , where , 6 and 7. For integers and , we prove the following. (i) A 4-GDD of type $…
Group divisible designs with block size 4 and type g^u m^1 - II
Anthony D. Forbes
We show that the necessary conditions for the existence of 4-GDDs of type g^u m^1 are sufficient for g congruent to 0 (mod h), h = 39, 51, 57, 69, 87, 93, and for g = 13, 17, 19, 2…
Theta Graph Designs
Anthony D. Forbes, Terry S. Griggs, Tamsin J. Forbes
We solve the design spectrum problem for all theta graphs with 10, 11, 12, 13, 14 and 15 edges
Designs for 24-vertex snarks
Anthony D. Forbes
The design spectrum problem is solved for the thirty-eight 24-vertex non-trivial snarks.
Snark Designs
Anthony D. Forbes
The main aim of this paper is to solve the design spectrum problem for Tietze's graph, the two 18-vertex Blanusa snarks, the six snarks on 20 vertices (including the flower snark J…