2019/02/27 by Hibi, Takayuki, Kanno, Hiroju, Matsuda, Kazunori · 1 citation
#05C69 #05C70 #05E40 #13D40 #13H10 #Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics
paper · doi:10.48550/arxiv.1902.10429
Let G be a finite simple graph on the vertex set V(G) = \x1, …, xn\ and I(G) ⊂ K[V(G)] its edge ideal, where K[V(G)] is the polynomial ring in x1, …, xn over a field K with each \rm deg xi = 1 and where I(G) is generated by those squarefree quadratic monomials xixj for which \xi, xj\ is an edge of G. In the present paper, given integers 1 ≤ a ≤ r and s ≥ 1, the existence of a finite connected simple graph G = G(a, r, d) with \rm im(G) = a, \rm reg(R/I(G)) = r and \rm deg hK[V(G)]/I(G) (λ) = s, where \rm im(G) is the induced matching number of G and where hK[V(G)]/I(G) (λ) is the h-polynomial of K[V(G)]/I(G).