Restricted antidirected subdivision conjecture for oriented graphs

Let DD be an oriented graph, and let δ(D)\delta(D) denote its minimum degree. For positive integers rr and ss, write Ks,s\vec{K}_{s,s} for the consistently oriented complete bipartite graph, and call an antidirected subdivision of a graph restricted when all its branch vertices are sources.

Restricted antidirected subdivision conjecture. Every oriented graph DD with

δ(D)f(2s,f(r,s))\delta(D) \geq f_{}(2s,f_{}(r,s))

contains a copy of Ks,s\vec{K}_{s,s} or an induced restricted antidirected subdivision of KrK_r.

This conjecture proposes a more precise version of the preceding minimum-degree result for oriented graphs. The supplied text does not indicate whether it has been resolved.

Sources & referencesView supporting material

Primary source

Arnab Char, Ken-ichi Kawarabayashi and Lucas Picasarri-Arrieta, “Edge-colouring and orientations: applications to degree- and χ-boundedness”, arXiv:2506.23054 (2026).

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