منابع مشابه
A Note on the Middle Levels Conjecture
The middle levels conjecture asserts that there is a Hamiltonian cycle in the middle two levels of 2k + 1-dimensional hypercube. The conjecture is known to be true for k ≤ 17 [I. Shields, B.J. Shields and C.D. Savage, Disc. Math., 309, 5271–5277 (2009)]. In this note, we verify that the conjecture is also true for k = 18 by constructing a Hamiltonian cycle in the middle two levels of 37-dimensi...
متن کاملAn update on the middle levels problem
The middle levels problem is to find a Hamilton cycle in the middle levels, M2k+1, of the Hasse diagram of B2k+1 (the partially ordered set of subsets of a 2k + 1element set ordered by inclusion). Previously, the best known, from [1], was that M2k+1 is Hamiltonian for all positive k through k = 15. In this note we announce that M33 and M35 have Hamilton cycles. The result was achieved by an alg...
متن کاملOn a lexical tree for the middle-levels graph problem
A conjecture of I. Hável asserts that all middle-levels graphs Mk of the (2k + 1)-cubes possess Hamilton cycles. In this work, a tree containing all vertices of certain reduced graphs of the Mk s is introduced and indicated via the Kierstead-Trotter lexical matchings, easing the algorithmic aspects of determining such Hamilton cycles, and here applied to the explicit presentation of some of the...
متن کاملA Note on Complementarity Problem
In this paper we prove a result of complementarity problem where compact condition is somewhat relaxed.
متن کاملA Note on the Two Cardinal Problem
In this note we prove a theorem concerning the two cardinal problem (see [l], [4], [6], [7] for reference and for some of the standard notation); this result has been referred to in [6, p. 311] and [7, (3.7) ]. The problem, first proposed by Vaught, is as follows. Let T be a first-order theory and let U be a unary predicate symbol in the language of T. T is said to admit the pair a, ß of cardin...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2016
ISSN: 0166-218X
DOI: 10.1016/j.dam.2015.08.001