Embedding Steiner triple systems in hexagon triple systems |
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Authors: | C.C. Lindner C.A. Rodger |
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Affiliation: | a Mathematics Department, Auburn University, Auburn, AL 36849-5307, USA b Dipartimento di Matematica, Università di Catantia, 95125 Catania, Italy |
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Abstract: | A hexagon triple is the graph consisting of the three triangles (triples) {a,b,c},{c,d,e}, and {e,f,a}, where a,b,c,d,e, and f are distinct. The triple {a,c,e} is called an inside triple. A hexagon triple system of order n is a pair (X,H) where H is a collection of edge disjoint hexagon triples which partitions the edge set of Kn with vertex set X. The inside triples form a partial Steiner triple system. We show that any Steiner triple system of order n can be embedded in the inside triples of a hexagon triple system of order approximately 3n. |
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Keywords: | Steiner triple systems Embedding 6-cycles |
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