scholarly journals Testing branch-width

2007 ◽  
Vol 97 (3) ◽  
pp. 385-393 ◽  
Author(s):  
Sang-il Oum ◽  
Paul Seymour
Keyword(s):  
Branch Width

scholarly journals Obstructions for Bounded Branch-depth in Matroids

2021 ◽  
Author(s):  
Jochen Pascal Gollin ◽  
Kevin Hendrey ◽  
Dillon Mayhew ◽  
Sang-il Oum
Keyword(s):  
Finite Field ◽  
Natural Analogue ◽  
Large Branch ◽  
Branch Width ◽  
Cycle Matroid ◽  
Fan Graph ◽  
A Minor

DeVos, Kwon, and Oum introduced the concept of branch-depth of matroids as a natural analogue of tree-depth of graphs. They conjectured that a matroid of sufficiently large branch-depth contains the uniform matroid Un;2n or the cycle matroid of a large fan graph as a minor. We prove that matroids with sufficiently large branch-depth either contain the cycle matroid of a large fan graph as a minor or have large branch-width. As a corollary, we prove their conjecture for matroids representable over a fixed finite field and quasi-graphic matroids, where the uniform matroid is not an option.

Dominating Sets in Planar Graphs: Branch-Width and Exponential Speed-Up

2006 ◽  
Vol 36 (2) ◽  
pp. 281-309 ◽  
Author(s):  
Fedor V. Fomin ◽  
Dimitrios M. Thilikos
Keyword(s):  
Planar Graphs ◽  
Dominating Sets ◽  
Speed Up ◽  
Branch Width

A Parametrized Algorithm for Matroid Branch-Width

2005 ◽  
Vol 35 (2) ◽  
pp. 259-277 ◽  
Author(s):  
Petr Hlinený
Keyword(s):  
Branch Width
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