Clique Vectors of $k$-Connected Chordal Graphs

Afshin Goodarzi

Clique Vectors of $k$-Connected Chordal Graphs

Combinatorics 2014-12-30 v2

Authors: Afshin Goodarzi

Abstract

The clique vector $\mathfrak{c}(G)$ of a graph $G$ is the sequence $(c_1, c_2, \ldots,c_d)$ 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.

Keywords

clique vector chordal graphs k-connected graphs commutative algebra graph theory cliques combinatorics

Cite

@article{arxiv.1403.6210,
  title  = {Clique Vectors of $k$-Connected Chordal Graphs},
  author = {Afshin Goodarzi},
  journal= {arXiv preprint arXiv:1403.6210},
  year   = {2014}
}

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