Cohen-Macaulay edge ideal whose height is half of the number of vertices
نویسندگان
چکیده
منابع مشابه
Cohen-macaulay Edge Ideal Whose Height Is Half of the Number of Vertices
We consider a class of graphs G such that the height of the edge ideal I(G) is half of the number ♯V (G) of the vertices. We give Cohen-Macaulay criteria for such graphs.
متن کاملMORE GRAPHS WHOSE ENERGY EXCEEDS THE NUMBER OF VERTICES
The energy E(G) of a graph G is equal to the sum of the absolute values of the eigenvalues of G. Several classes of graphs are known that satisfy the condition E(G) > n , where n is the number of vertices. We now show that the same property holds for (i) biregular graphs of degree a b , with q quadrangles, if q<= abn/4 and 5<=a < b = 0 (iii) triregular graphs of degree 1, a, b that are quadran...
متن کاملThe Essential Ideal Is a Cohen–macaulay Module
Let G be a finite p-group which does not contain a rank two elementary abelian p-group as a direct factor. Then the ideal of essential classes in the mod-p cohomology ring of G is a Cohen–Macaulay module whose Krull dimension is the p-rank of the centre of G. This basically answers in the affirmative a question posed by J. F. Carlson (Question 5.4 in [7]).
متن کاملSequentially Cohen-macaulay Edge Ideals
Let G be a simple undirected graph on n vertices, and let I(G) ⊆ R = k[x1, . . . , xn] denote its associated edge ideal. We show that all chordal graphs G are sequentially Cohen-Macaulay; our proof depends upon showing that the Alexander dual of I(G) is componentwise linear. Our result complements Faridi’s theorem that the facet ideal of a simplicial tree is sequentially Cohen-Macaulay and impl...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Nagoya Mathematical Journal
سال: 2011
ISSN: 0027-7630,2152-6842
DOI: 10.1017/s002776300002612x