Wv paths on 3-polytopes
نویسندگان
چکیده
منابع مشابه
Monotone paths on polytopes
We investigate the vertex-connectivity of the graph of f -monotone paths on a d-polytope P with respect to a generic functional f . The third author has conjectured that this graph is always (d − 1)-connected. We resolve this conjecture positively for simple polytopes and show that the graph is 2-connected for any d-polytope with d ≥ 3. However, we disprove the conjecture in general by exhibiti...
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The Holt-Klee Condition states that there exist at least d vertex-disjoint strictly monotone paths from the source to the sink of a polytopal digraph consisting of the set of vertices and arcs of a polytope P directed by a linear objective function in general position. Studying these paths has the potential to provide new insight into a long standing problem, that of designing a polynomial-time...
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TheMonotone Upper Bound Problem (Klee, 1965) asks if the numberM(d, n) of vertices in a monotone path along edges of a d-dimensional polytope with n facets can be as large as conceivably possible: Is M(d, n) = Mubt(d, n), the maximal number of vertices that a d-polytope with n facets can have according to the Upper Bound Theorem? We show that in dimension d = 4, the answer is “yes”, despite the...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory
سال: 1969
ISSN: 0021-9800
DOI: 10.1016/s0021-9800(69)80007-4