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Mortezaeefar, Nazli Besharati","submitted_at":"2010-05-25T07:23:11Z","abstract_excerpt":"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 $G$. 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