The complement of a d-tree is Cohen-Macaulay

Abstract

In this work we obtain the result that the complement of a $d$-tree is a Cohen-Macaulay graph. To do this we use a theorem by Fröberg that estabilishes a condition for a Stanley-Reisner ring of a simplicial complex to be Cohen-Macaulay and a useful lemma to pass from a Stanley-Reisner ideal of a simplicial complex to an edge ideal of a graph.