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Petrosyan","submitted_at":"2009-11-23T18:26:31Z","abstract_excerpt":"An edge coloring of a graph $G$ with colors $1,2,\\ldots ,t$ is called an interval $t$-coloring if for each $i\\in \\{1,2,\\ldots,t\\}$ there is at least one edge of $G$ colored by $i$, and the colors of edges incident to any vertex of $G$ are distinct and form an interval of integers. A graph $G$ is interval colorable, if there is an integer $t\\geq 1$ for which $G$ has an interval $t$-coloring. Let $\\mathfrak{N}$ be the set of all interval colorable graphs. In 2004 Kubale and Giaro showed that if $G,H\\in \\mathfrak{N}$, then the\n  Cartesian product of these graphs belongs to $\\mathfrak{N}$. 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