r-regular digraphs satisfy c(D) >= ceil(3r/22) with an improved upper bound, and have directed tree-width Omega(r), yielding corollaries on cylindrical wall subdivisions.
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Openly disjoint cycles and directed tree-width of regular digraphs
r-regular digraphs satisfy c(D) >= ceil(3r/22) with an improved upper bound, and have directed tree-width Omega(r), yielding corollaries on cylindrical wall subdivisions.