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math.CO2025
Closure property of contraction-depth of matroids
Marcin Brianski, Daniel Kral, Ander Lamaison
Contraction-depth is a matroid depth parameter analogous to tree-depth of graphs. We establish the matroid analogue of the classical graph theory result asserting that the tree…
math.CO2024
Four-coloring Eulerian triangulations of the torus
Marcin Brianski, Daniel Kral, Ander Lamaison +1
Hutchinson, Richter and Seymour [J. Combin. Theory Ser. B 84 (2002), 225-239] showed that every Eulerian triangulation of an orientable surface that has a sufficiently high represe…
math.CO2024
Branch-depth is minor closure of contraction-deletion-depth
Marcin BriaÅski, Daniel Kráľ, Kristýna Pekárková
The notion of branch-depth for matroids was introduced by DeVos, Kwon and Oum as the matroid analogue of the tree-depth of graphs. The contraction-deletion-depth, another tree-dept…