Treewidth, pathwidth and cospan decompositions with applications to graph-accepting tree automata

Abstract We will revisit the categorical notion of cospan decompositions of graphs and compare it to the well-known notions of path decomposition and tree decomposition from graph theory. More specifically, we will define several types of cospan decompositions with appropriate width measures and show that these width measures coincide with pathwidth and treewidth. Such graph decompositions of small width are used to efficiently decide graph properties, for instance via graph automata. Hence we will give an application by defining graph-accepting tree automata, thus integrating previous work by Courcelle into the setting of cospan decompositions. Furthermore we will show that regardless of whether we consider path or tree decompositions, we arrive at the same notion of recognizability.