A Note on Directed Treewidth [article]

Sebastian Wiederrecht
2019 arXiv   pre-print
We characterise digraphs of directed treewidth one in terms of forbidden butterfly minors. Moreover, we show that there is a linear relation between the hypertree-width of the dual of the cycle hypergraph of D, i. e. the hypergraph with vertices V (D) where every hyperedge corresponds to a directed cycle in D, and the directed treewidth of D. Based on this we show that a digraph has directed treewidth one if and only if its cycle hypergraph is a hypertree.
arXiv:1910.01826v1 fatcat:7t6hzfy3gbhmdnckzhjav5iuve