论文标题
通过匹配，任何Steiner三重系统的最小嵌入到3-SUN系统中
Minimum embedding of any Steiner triple system into a 3-sun system via matchings
论文作者
论文摘要
让$ g $是一个简单的有限图，$ g'$是$ g $的子图。 a $ g'$ - 设计$（x，\ cal b）$ n $的$ n $ n $嵌入到$ g $ -design $（x \ cup u，\ cal c）$ n+u $的订单$ f：\ cal b \ cal b \ rightarrow \ cal c $ c $ b $ a $ b $ a $ b）中$ b $ b cal b cal b cal ba $ b）函数$ f $称为$（x，\ cal b）$的嵌入到$（x \ cup u，\ cal c）$中。如果$ u $达到最低值，则$ f $是最低嵌入。 Here, by means of König's Line Coloring Theorem and edge coloring properties a complete solution is given to the problem of determining a minimum embedding of any $K_3$-design (well-known as Steiner Triple System or, shortly, STS) into a 3-sun system or, shortly, a 3SS (i.e., a $G$-design where $G$ is a graph on six vertices consisting of a triangle with three形成1因子的吊坠边缘。
Let $G$ be a simple finite graph and $G'$ be a subgraph of $G$. A $G'$-design $(X,\cal B)$ of order $n$ is said to be embedded into a $G$-design $(X\cup U,\cal C)$ of order $n+u$, if there is an injective function $f:\cal B\rightarrow \cal C$ such that $B$ is a subgraph of $f(B)$ for every $B\in\cal B$. The function $f$ is called an embedding of $(X,\cal B)$ into $(X\cup U,\cal C)$. If $u$ attains the minimum possible value, then $f$ is a minimum embedding. Here, by means of König's Line Coloring Theorem and edge coloring properties a complete solution is given to the problem of determining a minimum embedding of any $K_3$-design (well-known as Steiner Triple System or, shortly, STS) into a 3-sun system or, shortly, a 3SS (i.e., a $G$-design where $G$ is a graph on six vertices consisting of a triangle with three pendant edges which form a 1-factor).
