Clique Vectors of $k$-Connected Chordal Graphs

Abstract

The clique vector $\mathfrak{c}(G)$ of a graph $G$ is the sequence $(c_1,c_2,\dots ,c_d)$ in ${\mathbb{N}}^d$, where $c_i$ is the number of cliques in $G$ with $i$ vertices and $d$ is the largest cardinality of a clique in $G$. In this note, we use tools from commutative algebra to characterize all possible clique vectors of $k$-connected chordal graphs.

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