Maximum packing for perfect four-triple configurations Original Research Article

The graph consisting of the four 3-cycles (triples) image, and image, where imageʹs are distinct, is called a 4-cycle-triple block and the 4-cycle image of the 4-cycle-triple block is called the interior (inside) 4-cycle. The graph consisting of the four 3-cycles image, and image, where imageʹs are distinct, is called a kite-triple block and the kite image-image (formed by a 3-cycle with a pendant edge) is called the interior kite. A decomposition of image into 4-cycle-triple blocks (or into kite-triple blocks) is said to be perfect if the interior 4-cycles (or kites) form a k-fold 4-cycle system (or kite system). A packing of image with 4-cycle-triples (or kite-triples) is a triple image, where X is the vertex set of image, B is a collection of 4-cycle-triples (or kite-triples), and L is a collection of 3-cycles, such that image partitions the edge set of image. If image is as small as possible, or equivalently image is as large as possible, then the packing image is called maximum. If the maximum packing image with 4-cycle-triples (or kite-triples) has the additional property that the interior 4-cycles (or kites) plus a specified subgraph of the leave L form a maximum packing of image with 4-cycles (or kites), it is said to be perfect.