Abstract
The Holt–Klee theorem says that the graph of a d-polytope, with edges oriented by a linear function on P that is not constant on any edge, admits d independent monotone paths from the source to the sink. We prove that the digraphs obtained from oriented matroid programs of rank d+1 on n+2 elements, which include those from d-polytopes with n facets, admit d independent monotone paths from source to sink if d≤4. This was previously only known to hold for d≤3 and n≤6.
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