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Cohen–Macaulay Rings Associated with Digraphs

✍ Scribed by Kazufumi Eto

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
171 KB
Volume
206
Category
Article
ISSN
0021-8693

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✦ Synopsis

Let G be a digraph, that is, a pair of sets consisting of a set of vertices Ž . and a set of directed edges for a more precise definition, see Section 3 . It is an interesting problem to know how to count the Hamilton cycles of G, that is, cycles containing all vertices of G. In this paper, we will give the upper bound of the number of them by using the theory of commutative rings. It is natural to assume that G is strongly connected, otherwise there is no Hamilton cycle. The way to give it is to associate G with a Cohen᎐Macaulay ring which is positively graded of dimension 1 and to compute its Macaulay type. In fact, the associated ring is a monoid ring, r

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