Perfect hexagon triple systems

✍ Scribed by Selda Küçükçifçi; C.C Lindner

• Book ID: 104113340
• Publisher: Elsevier Science
• Year: 2004
• Tongue: English
• Weight: 323 KB
• Volume: 279
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/s0012-365x(03)00278-4

✦ Synopsis

The graph consisting of the three 3-cycles (a; b; c), (c; d; e), and (e; f; a), where a; b; c; d; e, and f are distinct is called a hexagon triple. The 3-cycle (a; c; e) is called an "inside" 3-cycle; and the 3-cycles (a; b; c), (c; d; e), and (e; f; a) are called "outside" 3-cycles. A 3k-fold hexagon triple system of order n is a pair (X; C), where C is an edge disjoint collection of hexagon triples which partitions the edge set of 3kKn. Note that the outside 3-cycles form a 3k-fold triple system. If the hexagon triple system has the additional property that the collection of inside 3-cycles (a; c; e) is a k-fold triple system it is said to be perfect. A perfect maximum packing of 3kKn with hexagon triples is a triple (X; C; L), where C is a collection of edge disjoint hexagon triples and L is a collection of 3-cycles such that the insides of the hexagon triples plus the inside of the triangles in L form a maximum packing of kKn with triangles. This paper gives a complete solution (modulo two possible exceptions) of the problem of constructing perfect maximum packings of 3kKn with hexagon triples.