Parameters Related to Tree-Width, Zero Forcing, and Maximum Nullity of a Graph
Tree-width, and variants that restrict the allowable tree decompositions, play an important role in the study of graph algorithms and have application to computer science. The zero forcing number is used to study the maximum nullity/minimum rank of the family of symmetric matrices described by a graph. We establish relationships between these parameters, including several Colin de Verdire type parameters, and introduce numerous variations, including the minor monotone floors and ceilings of some of these parameters. This leads to new graph parameters and to new characterizations of existing graph parameters. In particular, tree-width, largeur d'arborescence, path-width, and proper path-width are each characterized in terms of a minor monotone floor of a certain zero forcing parameter defined by a color change rule.
maximum nullity zero forcing number minimum rank colin de verdire type parameter minor monotone floor path-width tree-width minor monotone ceiling 05c50 05c85 05c83 15a03 15a18 05c40 05c75 68r10