Obstructions to Within a Few Vertices or Edges of Acyclic
نویسندگان
چکیده
Finite obstruction sets for lower ideals in the minor order are guaranteed to exist by the Graph Minor Theorem. It has been known for several years that, in principle, obstruction sets can be mechanically computed for most natural lower ideals. In this paper, we describe a general-purpose method for nding obstructions by using a bounded treewidth (or pathwidth) search. We illustrate this approach by characterizing certain families of cycle-cover graphs based on the two well-known problems: k-Feedback Vertex Set and k-Feedback Edge Set. Our search is based on a number of algorithmic strategies by which large constants can be mitigated, including a randomized strategy for obtaining proofs of minimality.
منابع مشابه
Properly orderable graphs
In a graph G = (V, E) provided with a linear order ”<” on V , a chordless path with vertices a, b, c, d and edges ab, bc, cd is called an obstruction if both a < b and d < c hold. Chvátal [2] defined the class of perfectly orderable graphs (i.e., graphs possessing an acyclic orientation of the edges such that no obstruction is induced) and proved that they are perfect. We introduce here the cla...
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