On the chordality of a graph
Terry A. McKee, Edward R. Scheinerman · Journal of Graph Theory · 1993
Abstract The chordality of a graph G = ( V, E ) is defined as the minimum k such that we can write E = E 1 ∩ … ∩ E k with each ( V, E i ) a chordal graph. We present several results bounding the value of this generalization of boxicity. Our principal result is that the chordality of a graph is at most its tree width. In particular, series‐parallel graphs have chordality at most 2. Potential strengthenings of this statement fail in that there are planar graphs with chordality 3 and series‐parallel graphs with boxicity 3. © 1993 John Wiley & Sons, Inc.