Non-vanishingness of Betti numbers of edge ideals

2011/10/11 by Kyouko Kimura, Kimura, Kyouko · 1 citation
Computer Science · Mathematics · #13D02 #13F55 (Primary) 05C99 (Secondary) #Algebraic structures and combinatorial models #Combinatorics (math.CO) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1110.2333

openalex publication_date 2011/10/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given finite simple graph one can associate the edge ideal. In this paper we discuss the non-vanishingness of the graded Betti numbers of edge ideals in terms of the original graph. In particular, we give a necessary and sufficient condition for a chordal graph on which the graded Betti number does not vanish and characterize the graded Betti number for a forest. Moreover we characterize the projective dimension for a chordal graph.

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• The vertex covers, Betti numbers and projective dimensions of perfect binary trees

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