We present a new algorithm that can output the rank-decomposition of width at most k of a graph if such exists. For that we use an algorithm that, for an input matroid represented over a fixed finite… (More)

We introduce “matroid parse trees” which, using only a limited amount of information at each node, can build up the vector representations of matroids of bounded branch-width over a finite field. We… (More)

We show that the tree-width of a graph can be defined without reference to graph vertices, and hence the notion of tree-width can be naturally extended to matroids. (This extension was inspired by an… (More)

Branch-width is a structural parameter very closely related to tree-width, but branch-width has an immediate generalization from graphs to matroids. We present an algorithm that, for a given matroid… (More)

Rank-width is a structural graph measure introduced by Oum and Seymour and aimed at better handling of graphs of bounded clique-width. We propose a formal framework and tools for easy design of… (More)

It has been proved by the author that all matroid properties definable in the monadic second-order (MSO) logic can be recognized in polynomial time for matroids of bounded branch-width which are… (More)

PETR HLINĚNÝ1,2,*, SANG-IL OUM3,7, DETLEF SEESE4 AND GEORG GOTTLOB5,6 Faculty of Informatics, Masaryk University, Botanická 68a, 602 00 Brno, Czech Republic VŠB, Technical University of Ostrava,… (More)

Abstract. Hliněný and Whittle have shown that the traditional treewidth notion of a graph can be defined without an explicit reference to vertices, and that it can be naturally extended to all… (More)

It was proved by [Garey and Johnson, 1983] that computing the crossing number of a graph is an NP -hard problem. Their reduction, however, used parallel edges and vertices of very high degrees. We… (More)