In this note we introduce algebraic tools for finding interesting classes of graphs G of linear type. In particular, when the symmetric algebra of the edge ideal of G is an integral domain, then necessarily G is of linear type. In this way it is proved that graphs of linear type are all the simple graphs with at most three edges, and all the simple graphs with no even cycles and vertex covering number 3.
GRAPHS OF LINEAR TYPE
IMBESI, Maurizio;
2006-01-01
Abstract
In this note we introduce algebraic tools for finding interesting classes of graphs G of linear type. In particular, when the symmetric algebra of the edge ideal of G is an integral domain, then necessarily G is of linear type. In this way it is proved that graphs of linear type are all the simple graphs with at most three edges, and all the simple graphs with no even cycles and vertex covering number 3.File in questo prodotto:
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