An algebraic property of the totally symmetric loops associated with Kirkman-Steiner triple systems

The chromatic index of block intersection graphs of Kirkman triple systems and cyclic Steiner triple systems

The block intersection graph of a combinatorial design with block set B is the graph with B as its vertex set such that two vertices are adjacent if and only if their associated blocks are not disjoint. The chromatic index of a graph G is the least number of colours that enable each edge of G to be assigned a single colour such that adjacent edges never have the same colour. A graph G for which...

Intersection Numbers of Kirkman Triple Systems

A Steiner triple system of order v (briefly STS(v)) is a pair (X, B) where X is a v-set and B is a collection of 3-subset of X (called triple) such that every pair of distinct elements of X belongs to exactly one triple of B. A Kirkman triple system of order v (briefly KTS(v)) is a Steiner triple system of order v (X, B) together with a partition R of the set of triples B into subsets R1 , R2 ,...

Kirkman triple systems of order 21 with nontrivial automorphism group

There are 50,024 Kirkman triple systems of order 21 admitting an automorphism of order 2. There are 13,280 Kirkman triple systems of order 21 admitting an automorphism of order 3. Together with the 192 known systems and some simple exchange operations, this leads to a collection of 63,745 nonisomorphic Kirkman triple systems of order 21. This includes all KTS(21)s having a nontrivial automorphi...

A Completion Conjecture for Kirkman Triple Systems

Further results on nearly Kirkman triple systems with subsystems

In this paper we further discuss the embedding problem for nearly Kirkman triple systems and get the result that: (1) For u ≡ v ≡ 0 (mod 6), v¿ 78, and u¿ 3:5v, there exists an NKTS(u) containing a sub-NKTS(v). (2) For v = 18; 24; 30; 36; 42; 48; 54; 60; 66 or 72, there exists an NKTS(u) containing a sub-NKTS(v) if and only if u ≡ 0 (mod 6) and u¿ 3v. c © 2002 Elsevier B.V. All rights reserved.