Forbidden Directed Minors and Directed Pathwidth
نویسندگان
چکیده
Undirected graphs of pathwidth at most one are characterized by two forbidden minors i.e., (i) K3 the complete graph on three vertices and (ii) S2,2,2 the spider graph with three legs of length two each [BFKL87]. Directed pathwidth is a natural generalization of pathwidth to digraphs. In this paper, we prove that digraphs of directed pathwidth at most one are characterized by a finite number of forbidden directed minors. To achieve our goal, we present a new decomposition theorem for digraphs of directed pathwidth ≥ 2 and prove several properties of the forbidden directed minors, which are of independent interest.
منابع مشابه
Forbidden directed minors and Kelly-width
Partial 1-trees are undirected graphs of treewidth at most one. Similarly, partial 1-DAGs are directed graphs of KellyWidth at most two. It is well-known that an undirected graph is a partial 1-tree if and only if it has no K3 minor. In this paper, we generalize this characterization to partial 1-DAGs. We show that partial 1-DAGs are characterized by three forbidden directed minors, K3, N4 and M5.
متن کاملCharacterization of graphs and digraphs with small process numbers
We introduce the process number of a digraph as a tool to study rerouting issues in wdm networks. This parameter is closely related to the vertex separation (or pathwidth). We consider the recognition and the characterization of (di)graphs with small process number. In particular, we give a linear time algorithm to recognize (and process) graphs with process number at most 2, along with a chara...
متن کاملExploiting Parse Trees for Graphs of Bounded Treewidth
This thesis studies a structural framework for representing graphs of bounded treewidth, called a [treewidth] t-parse. This is a natural extension of the Cattell–Dinneen [pathwidth] t-parses, which they used in their platform for finding forbidden minors. Our t-parses are quite useful for representing graphs (in parsed form) for the many dynamic programs that are available for graphs of bounded...
متن کاملAn Upper Bound on the Size of Obstructions for Bounded Linear Rank-Width
We provide a doubly exponential upper bound in p on the size of forbidden pivot-minors for symmetric or skew-symmetric matrices over a fixed finite field F of linear rank-width at most p. As a corollary, we obtain a doubly exponential upper bound in p on the size of forbidden vertex-minors for graphs of linear rank-width at most p. This solves an open question raised by Jeong, Kwon, and Oum [Ex...
متن کاملForbidden minors to graphs with small feedback sets
Finite obstruction set characterizations for lower ideals in the minor order are guaranteed to exist by the Graph Minor Theorem. In this paper we characterize several families of graphs with small feedback sets, namely k1-Feedback Vertex Set, k2-Feedback Edge Set and (k1,k2){Feedback Vertex/Edge Set, for small integer parameters k1 and k2. Our constructive methods can compute obstruction sets f...
متن کامل