K. Kimura

activity

20092020

a

-invariant of Cameron--Walker graphs

14 citations · 24 across the 15 of their papers we have counts for

collaborators

Showing math.ACShow all

12 papers · 1 filter

math.AC2020★ 1 cited

Homological invariants of Cameron--Walker graphs

Takayuki Hibi, Hiroju Kanno, Kyouko Kimura +2

Let $G$ be a finite simple connected graph on $[n]$ and $R = K [x_{1}, \dots, x_{n}]$ the polynomial ring in $n$ variables over a field $K$ . The edge ideal of $G$ is the ideal $I (G)$ o…

math.AC2019★ 14 cited

Regularity and $a$ -invariant of Cameron--Walker graphs

Takayuki Hibi, Kyouko Kimura, Kazunori Matsuda +1

Let $S$ be the polynomial ring over a field $K$ and $I \subset S$ a homogeneous ideal. Let $h (S / I, λ)$ be the $h$ -polynomial of $S / I$ and $s = deg h (S / I, λ)$ the degree of $…

math.AC2018

Extremal Betti numbers of edge ideals

Takayuki Hibi, Kyouko Kimura, Kazunori Matsuda

Given integers $r$ and $b$ with $1 \leq b \leq r$ , a finite simple connected graph $G$ for which $reg (S / I (G)) = r$ and the number of extremal Betti numbers of $S / I (G)$ is equ…

math.AC2014

Arithmetical rank of strings and cycles

Kyouko Kimura, Paolo Mantero

Let $R$ be a polynomial ring over a field $K$ . To a given squarefree monomial ideal $I \subset R$ , one can associate a hypergraph $H (I)$ . In this article, we prove that the arithme…

math.AC2013★ 2 cited

Algebraic study on Cameron-Walker graphs

Takayuki Hibi, Akihiro Higashitani, Kyouko Kimura +1

Let $G$ be a finite simple graph on $[n]$ and $I (G) \subset S$ the edge ideal of $G$ , where $S = K [x_{1}, \dots, x_{n}]$ is the polynomial ring over a field $K$ . Let $m (G)$ denote…

math.AC2013

Non-vanishing of Betti numbers of edge ideals and complete bipartite subgraphs

Kyouko Kimura

Given a finite simple graph one can associate the edge ideal. In this paper we prove that a graded Betti number of the edge ideal does not vanish if the original graph contains a s…