均衡型C_k-Foilデザイン

In graph theory, the decomposition problem of graphs is a very important topic. Various type of decompositions of many graphs can be seen in the literature of gaph theory. Let k , t and n be positive integers (k ≧ 3, t ≧ 2). It is shown that the necessary and sufficient condition for the existence of a balanced C_k-t-foil decomposition of the complete graph K_n is n≡1 (mod 2kt) for k ＝ 11, 13, 15, 17, 19, 21, 23, 25. These decompositions are to be known as balanced C_k-foil designs