Alan Hartman, Dean G. Hoffman
European Journal of Combinatorics
A partial triple system of order v, PT(v), is pair (V, B) where V is a v-set, and B is a collection of 3-subsets of V (called triples) such that each 2-subset of V is contained in at most one triple. A maximum partial triple system of order v, MPT(v), is a PT(v), (V, B), such that for any other PT(v), (V, C), we have |C| {slanted equal to or less-than}|B|. Several authors have considered the problem of embedding PT(v) and MPT(v) in systems of higher order. We complete the proof, begun by Mendelsohn and Rosa [6], that an MPT(u) can be embedded in an MPT(v) where v is the smallest value in each congruence class mod 6 with v ≥ 2u. We also consider a general problem concerning transversals of minimum edge-colourings of the complete graph. © 1986.
Alan Hartman, Dean G. Hoffman
European Journal of Combinatorics
Ahmed M. Assaf, Alan Hartman, et al.
Discrete Mathematics
Alan Hartman, Andrei Kirshin, et al.
SEAPP 2002
Haim Hanani, Alan Hartman, et al.
Discrete Mathematics