The extended 1-perfect trades in small hypercubes
نویسنده
چکیده
An extended 1-perfect trade is a pair (T0, T1) of two disjoint binary distance-4 even-weight codes such that the set of words at distance 1 from T0 coincides with the set of words at distance 1 from T1. Such trade is called primary if any pair of proper subsets of T0 and T1 is not a trade. Using a computer-aided approach, we classify nonequivalent primary extended 1-perfect trades of length 10, constant-weight extended 1-perfect trades of length 12, and Steiner trades derived from them. In particular, all Steiner trades with parameters (5, 6, 12) are classified.
منابع مشابه
Perfect matchings extend to Hamilton cycles in hypercubes
Kreweras’ conjecture [1] asserts that any perfect matching of the hypercube Qd, d ≥ 2, can be extended to a Hamilton cycle. We prove this conjecture.
متن کاملMatching graphs of Hypercubes and Complete Bipartite Graphs
Kreweras’ conjecture [1] asserts that every perfect matching of the hypercube Qd can be extended to a Hamiltonian cycle. We [2] proved this conjecture but here we present a simplified proof. The matching graph M(G) of a graph G has a vertex set of all perfect matchings of G, with two vertices being adjacent whenever the union of the corresponding perfect matchings forms a Hamiltonian cycle. We ...
متن کاملPrescribed matchings extend to Hamiltonian cycles in hypercubes with faulty edges
Ruskey and Savage asked the following question: Does every matching of Qn for n ≥ 2 extend to a Hamiltonian cycle of Qn? J. Fink showed that the question is true for every perfect matching, and solved the Kreweras’ conjecture. In this paper we consider the question in hypercubes with faulty edges. We show that every matching M of at most 2n− 1 edges can be extended to a Hamiltonian cycle of Qn ...
متن کاملOn Perfect Dominating Sets in Hypercubes
The complements of the perfect dominating sets of the n-cube, for n $ 8, are characterized as well as some outstanding vertex-spanning edge-partitions of them involving the Fano plane, as a contribution to the study of distancepreserving regular subgraphs of hypercubes.
متن کاملOn Semi-perfect 1-Factorizations
The perfect 1-factorization conjecture by A. Kotzig [7] asserts the existence of a 1-factorization of a complete graph K2n in which any two 1-factors induce a Hamiltonian cycle. This conjecture is one of the prominent open problems in graph theory. Apart from its theoretical significance it has a number of applications, particularly in designing topologies for wireless communication. Recently, ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Discrete Mathematics
دوره 340 شماره
صفحات -
تاریخ انتشار 2017