# Homological invariants of Cameron–Walker Graphs

@article{Hibi2020HomologicalIO, title={Homological invariants of Cameron–Walker Graphs}, author={Takayuki Hibi and Hiroju Kanno and Kyouko Kimura and Kazunori Matsuda and Adam Van Tuyl}, journal={arXiv: Commutative Algebra}, year={2020} }

Let $G$ be a finite simple connected graph on $[n]$ and $R = K[x_1, \ldots, x_n]$ the polynomial ring in $n$ variables over a field $K$. The edge ideal of $G$ is the ideal $I(G)$ of $R$ which is generated by those monomials $x_ix_j$ for which $\{i, j\}$ is an edge of $G$. In the present paper, the possible tuples $(n, {\rm depth} (R/I(G)), {\rm reg} (R/I(G)), \dim R/I(G), {\rm deg} \ h(R/I(G)))$, where ${\rm deg} \ h(R/I(G))$ is the degree of the $h$-polynomial of $R/I(G)$, arising from Cameron…

## 7 Citations

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### The regularity and h-polynomial of Cameron-Walker graphs

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Fix an integer $n \geq 1$, and consider the set of all connected finite simple graphs on $n$ vertices. For each $G$ in this set, let $I(G)$ denote the edge ideal of $G$ in the polynomial ring $R =…

### Matchings and squarefree powers of edge ideals

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Squarefree powers of edge ideals are intimately related to matchings of the underlying graph. In this paper we give bounds for the regularity of squarefree powers of edge ideals, and we consider the…

### On the three graph invariants related to matching of finite simple graphs

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ABSTRACT. Let G be a finite simple graph on the vertex set V (G) and let ind-match(G), min-match(G) and match(G) denote the induced matching number, the minimum matching number and the matching…

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. Let pd( I ( G )) and reg( I ( G )) respectively denote the projective dimension and the regularity of the edge ideal I ( G ) of a graph G . For any positive integer n , we determine all pairs (pd(…

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