Decomposition of Complete graphs into Triangles and Claws

[[abstract]]Let Kn be a complete graph with n vertices, Ck denote a cycle of length k, and Sk denote a star with k edges. If k=3, then we call C3 a triangle and S3 a claw. In this paper, we show that for any nonnegative integers p and q and any positive integer n, there exists a decomposition of Kn into p copies of C3 and q copies of S3 if and only if 3(p+q)=(n2), q≠1,2 if n is odd, q=1 if n=4, and q≥max{3,⌈n4⌉} if n is even and n≥6.[[notice]]補正完畢[[journaltype]]國內[[incitationindex]]SCI[[ispeerreviewed]]Y[[booktype]]電子版[[countrycodes]]TW