Chordal graphs and the characteristic polynomial Original Research Article

A characteristic polynomial was recently defined for greedoids, generalizing the notion for matroids. When chordal graphs are viewed as antimatroids by shelling of simplicial vertices, the greedoid characteristic polynomial gives additional information about those graphs. In particular, the characteristic polynomial for a chordal graph is an alternating clique generating function and is expressible in terms of the clique decomposition of the graph. From it, one obtains an expression for the number of blocks in the graph in terms of clique sizes.