On the Holt-Klee property for oriented matroid programming

被引：0
|
作者：
Morris, Walter D., Jr. [1 ]
机构：
[1] George Mason Univ, Dept Math Sci, 4400 Univ Dr, Fairfax, VA 22030 USA
来源：
EUROPEAN JOURNAL OF COMBINATORICS | 2022年 / 101卷
关键词：
ORIENTATIONS; CONVEX; BOUNDS;
D O I：
10.1016/j.ejc.2021.103460
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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. (C) 2021 Elsevier Ltd. All rights reserved.
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页数：13
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