\max\{\mu(G_1),\mu(G_2)\}$
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On graph products and multi-word-representability
arXiv:2603.29629v4 Announce Type: replace-cross Abstract: The multi-word-representation number $\mu(G)$ of a graph $G$ is the minimum number of word-representable graphs whose union is $G$. We study the behavior of $\mu$ under six standard graph products: the lexicographic, Cartesian, rooted, corona, tensor, and strong products. For the Cartesian and rooted products, we show that $\mu(G_1 \square G_2)=\mu(G_1 \diamond G_2)=\max\{\mu(G_1),\mu(G_2)\}$. For the corona product, we prove that...
On graph products and multi-word-representability
arXiv:2603.29629v3 Announce Type: replace-cross Abstract: The multi-word-representation number $\mu(G)$ of a graph $G$ is the minimum number of word-representable graphs whose union is $G$. We study the behavior of $\mu$ under four standard graph products: the lexicographic, Cartesian, rooted, and corona products.