Steiner 2-设计的Silver块交图
Silver block intersection graphs of Steiner 2-designs
摘要：
对于块设计$\cal{D}$、一系列{ \sf块交图} $G_i$或$i$ -{ \rm BIG}（$\cal{D}$），定义$i=0, ..., k$，其中顶点是$\cal{D}$的块，当且仅当对应的块恰好相交于$i$元素时，两个顶点相邻。银图$G$是相对于$G$的最大独立集定义的，称为该图的{ \sf对角线}。设$G$是$r$ -正则的，$c$是$G$的一个真$(r + 1)$ -染色. $G$中的顶点$x$被称为相对于$c$的{ \sf rainbow}，如果每个颜色都出现在闭合邻域$N[x] = N(x) \cup \{x\}$中。给定$G$的对角线$I$，如果每个$x\in I$相对于$c$是彩虹，则称着色$c$相对于$I$是银色的。我们说$G$是{ \sf silver}，如果它允许相对于某些PDMATHAMY的银色着色。研究了Steiner体系${\cal{D}}=S(2,k,v)$的0-{ \rm BIG}（$\cal{D}$）和1-{ \rm BIG}（$\cal{D}$）为银的条件.
英文摘要：
For a block design $\cal{D}$, a series of {\sf block intersection graphs} $G_i$, or $i$-{\rm BIG}($\cal{D}$), $i=0, ..., k$ is defined in which the vertices are the blocks of $\cal{D}$, with two vertices adjacent if and only if the corresponding blocks intersect in exactly $i$ elements. A silver graph $G$ is defined with respect to a maximum independent set of $G$, called a {\sf diagonal} of that graph. Let $G$ be $r$-regular and $c$ be a proper $(r + 1)$-coloring of $G$. A vertex $x$ in $G$ is said to be {\sf rainbow} with respect to $c$ if every color appears in the closed neighborhood $N[x] = N(x) \cup \{x\}$. Given a diagonal $I$ of $G$, a coloring $c$ is said to be silver with respect to $I$ if every $x\in I$ is rainbow with respect to $c$. We say $G$ is {\sf silver} if it admits a silver coloring with respect to some $I$. We investigate conditions for 0-{\rm BIG}($\cal{D}$) and 1-{\rm BIG}($\cal{D}$) of Steiner systems ${\cal{D}}=S(2,k,v)$ to be silver.
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