Edge Ideals and the Cohen-Macaulay Property, M.Sc. Thesis Sharif University of Technology ; Pournaki, Mohammad Reza (Supervisor)
Abstract
set V = {1; : : : ; n}. Let K be a field and let S be the polynomial ring K[x1; : : : ; xn].The edge ideal I(G), associated to G, is the ideal of S generated by the set of squarefree monomials xi xj so that i is adjacent to j. The graph G is Cohen–Macaulay over K if S=I(G) is a Cohen–Macaulay ring. In this project we will explain Herzog-Hibi’s classification of all Cohen–Macaulay bipartite graphs
Cataloging briefEdge Ideals and the Cohen-Macaulay Property, M.Sc. Thesis Sharif University of Technology ; Pournaki, Mohammad Reza (Supervisor)
Abstract
set V = {1; : : : ; n}. Let K be a field and let S be the polynomial ring K[x1; : : : ; xn].The edge ideal I(G), associated to G, is the ideal of S generated by the set of squarefree monomials xi xj so that i is adjacent to j. The graph G is Cohen–Macaulay over K if S=I(G) is a Cohen–Macaulay ring. In this project we will explain Herzog-Hibi’s classification of all Cohen–Macaulay bipartite graphs
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