منابع مشابه
Proof of the middle levels conjecture
Define the middle layer graph as the graph whose vertex set consists of all bitstrings of length 2n + 1 that have exactly n or n + 1 entries equal to 1, with an edge between any two vertices for which the corresponding bitstrings differ in exactly one bit. The middle levels conjecture asserts that this graph has a Hamilton cycle for every n ≥ 1. This conjecture originated probably with Havel, B...
متن کاملA 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 کاملPartial proof of Graham Higman's conjecture related to coset diagrams
Graham Higman has defined coset diagrams for PSL(2,ℤ). These diagrams are composed of fragments, and the fragments are further composed of two or more circuits. Q. Mushtaq has proved in 1983 that existence of a certain fragment γ of a coset diagram in a coset diagram is a polynomial f in ℤ[z]. Higman has conjectured that, the polynomials related to the fragments are monic and for a fixed degree...
متن کاملA short proof of the middle levels theorem
Consider the graph that has as vertices all bitstrings of length 2n+1 with exactly n or n+1 entries equal to 1, and an edge between any two bitstrings that differ in exactly one bit. The well-known middle levels conjecture asserts that this graph has a Hamilton cycle for any n ≥ 1. In this paper we present a new proof of this conjecture, which is much shorter and more accessible than the origin...
متن کاملA short proof of the maximum conjecture in CR dimension one
In this paper and by means of the extant results in the Tanaka theory, we present a very short proof in the specific case of CR dimension one for Beloshapka's maximum conjecture. Accordingly, we prove that each totally nondegenerate model of CR dimension one and length >= 3 has rigidity. As a result, we observe that the group of CR automorphisms associated with each of such models contains onl...
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ژورنال
عنوان ژورنال: Proceedings of the London Mathematical Society
سال: 2016
ISSN: 0024-6115,1460-244X
DOI: 10.1112/plms/pdw004