An Inequality Characterizing Chordal Graphs

Terry A. McKee1
1Department of Mathematics & Statistics Wright State University, Dayton, Ohio 45435

Abstract

A simple inequality involving the number of components in an arbitrary graph becomes an equality precisely when the graph is chordal. This leads to a mechanism by which any graph parameter, if always at least as large as the number of components, corresponds to a subfamily of chordal graphs. As an example, the domination number corresponds to the well-studied family of \(P_4, C_4\)-free graphs.