2021/10/11 by Lourdes J. Cruz, Cruz, Lourdes, Enríque G. Reyes +3
Mathematics · #05C25 #05E40 #13F55 #13H10 #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Combinatorics (math.CO) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2110.05253
openalex publication_date 2021/10/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let G=(V,E) be a connected simple graph, with n vertices such that S is its homogeneous monomial subring. We prove that if S is normal and Gorenstein, then G is unmixed with cover number \lceil(n)/(2)\rceil and G has a strong \lceil(n)/(2)\rceil-τ-reduction. Furthermore, if n is even, then we show that G is bipartite. Finally, if S is normal and G is unmixed whose cover number is \lceil(n)/(2)\rceil, we give sufficient conditions for S to be Gorenstein.