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\input zb-ioport
\iteman{io-port 06090566}
\itemau{Hou, Yingtao; Kang, Qingde; Zhang, Yanli}
\itemti{The perfect $T (G)$-triple system for each subgraph $G$ of $K_5$ with eight edges.}
\itemso{Acta Math. Appl. Sin. 34, No. 5, 830-837 (2011).}
\itemab
Summary: Let $G$ be a subgraph of $K_n$. The graph obtained from $G$ by replacing each edge with a 3-cycle whose third vertex is distinct from other vertices in the configuration is called a $T (G)$-triple. An edge-disjoint decomposition of $3K_n$ into copies of $T (G)$ is called a $T (G)$-triple system of order $n$. If, in each copy of $T (G)$ in a $T (G)$-triple system, one edge is taken from each 3-cycle (chosen so that these edges form a copy of $G$) in such a way that the resulting copies of $G$ form an edge-disjoint decomposition of $K_n$, then the $T (G)$-triple system is said to be perfect. The set of positive integers $n$ for which a perfect $T (G)$-triple system exists is called its spectrum. A series of earlier papers determined the spectra for cases where $G$ is any subgraph of $K_4$. Then, in our previous paper, the spectrum of perfect $T (G)$-triple systems for each graph $G$ with five vertices and $i (\leq 7)$ edges is determined. In this paper, we completely solve the spectrum problem of the perfect $T (G)$-triple system for each subgraph $G$ of $K_5$ with eight edges.
\itemrv{~}
\itemcc{}
\itemut{triple system; perfect graphs}
\itemli{}
\end