Several notions of rank-width for countable graphs
Résumé
We define several notions of rank-width for countable graphs. We compare, for each of them the width of a countable graph with the least upper-bound of the widths of its finite induced subgraphs. A width has the compactness property if these two values are equal. Our notion of rank-width that uses quasi-trees (trees where paths may have the order type of rational numbers) has this property. So has linear rank-width, based on arbitrary linear orders. A more natural notion of rank-width based on countable cubic trees (we call it discrete rank-width has a weaker type of compactness: the corresponding width is at most twice the least upper bound of the widths of the finite induced subgraphs. The notion of discrete linear rank-width, based on discrete linear orders has no compactness property.
Domaines
Logique en informatique [cs.LO]
Origine : Fichiers produits par l'(les) auteur(s)
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