5 Result(s)
within
Sang-il Oum
Data Structures
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Chapter and Conference Paper
Computing Small Pivot-Minors
A graph G contains a graph H as a pivot-minor if H can be obtained from G by applying a sequence of vertex deletions and edge pivots. Pivot-minors play an important role in the study of rank-width. However, so fa...
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Chapter and Conference Paper
An FPT 2-Approximation for Tree-cut Decomposition
The tree-cut width of a graph is a graph parameter defined by Wollan [J. Comb. Theory, Ser. B, 110:47–66, 2015] with the help of tree-cut decompositions. In certain cases, tree-cut width appears to be more adequa...
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Chapter and Conference Paper
Unifying Duality Theorems for Width Parameters in Graphs and Matroids (Extended Abstract)
We prove a general duality theorem for width parameters in combinatorial structures such as graphs and matroids. It implies the classical such theorems for path-width, tree-width, branch-width and rank-width, ...
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Chapter and Conference Paper
Finding Branch-Decompositions and Rank-Decompositions
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 field, outpu...
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Chapter and Conference Paper
Approximating Rank-Width and Clique-Width Quickly
Rank-width is defined by Seymour and the author to investigate clique-width; they show that graphs have bounded rank-width if and only if they have bounded clique-width. It is known that many hard graph proble...
