-- Criteria of belonging of a non-degenerate transportation polytope with a given number of faces (of maximum dimension) to the dass of polytopes with the minimum number of fc-faces of all dimensions (beginning with zero)'are suggested. A formula for this number is obtained. 1. INTRODUCTION One of the basic problems of combinatorial theory of polyhedra (going back to Euler) deals with the description of the range of values of the vector function f(M) = (/o(M), /i(M),..., fd-i(M)) whose fcth component is equal to the number of Maces of a d-polyhedron M. Up to now this problem is solved only for the classes of d-polyhedra with the number of vertices not greater than d + 3, and also for polytopes of different combinatorial types: Simplexes, prisms, pyramids . The problem of estimating the bounds for the variation of components of the vector f(M), provided that the other components are fixed, is also known (see [1, 2]). Most often the number of faces (of maximum dimension) is fixed, and one tries to obtain bounds for the other components. Such investigations are carried out both for abstract polyhedra and for the polyhedra of some combinatorial optimization problems. A criterion of belonging
Discrete Mathematics and Applications – de Gruyter
Published: Jan 1, 1993
It’s your single place to instantly
discover and read the research
that matters to you.
Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.
All for just $49/month
Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly
Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.
Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.
Read from thousands of the leading scholarly journals from SpringerNature, Wiley-Blackwell, Oxford University Press and more.
All the latest content is available, no embargo periods.
“Hi guys, I cannot tell you how much I love this resource. Incredible. I really believe you've hit the nail on the head with this site in regards to solving the research-purchase issue.”Daniel C.
“Whoa! It’s like Spotify but for academic articles.”@Phil_Robichaud
“I must say, @deepdyve is a fabulous solution to the independent researcher's problem of #access to #information.”@deepthiw
“My last article couldn't be possible without the platform @deepdyve that makes journal papers cheaper.”@JoseServera