id: 06090566
dt: j
an: 06090566
au: Hou, Yingtao; Kang, Qingde; Zhang, Yanli
ti: The perfect $T (G)$-triple system for each subgraph $G$ of $K_5$ with eight
    edges.
so: Acta Math. Appl. Sin. 34, No. 5, 830-837 (2011).
py: 2011
pu: Institute of Applied Mathematics, The Chinese Academy of Sciences, Beijing
la: ZH
cc: 
ut: triple system; perfect graphs
ci: 
li: 
ab: 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.
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