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The nice perfect-elimination characterization of graph polynomials
Nice perfect-elimination conjecture. The polynomial $R_G(q)$ can be factorized as a product of $q$ -numbers if and only if the graph $G$ has a nice perfect elimination order.
Conjectureopengraph-theory perfect-elimination-ordersarXiv posted 2 days ago

The nice perfect-elimination characterization of graph polynomials