For every perfect matching P of the hypercube Qd, d ≥ 2, there exists a perfect matching R such that P ∪ R is a Hamilton cycle of Qd. In fact, we prove the following theorem which is clearly stronger than the above and so implies Kreweras' conjecture. Let KQd be the complete graph on the vertices of the hypercube Qd.
Any perfect matching of the hypercube , , can be extended to a Hamilton cycle. We prove this conjecture.
In this paper, we prove that every perfect matching of Q n for n ≥ 4 can be extended to at least 2 2 n − 4 different hamiltonian cycles of Q n . Previous ...
Nov 13, 2009 · This is a known open problem. See "Matchings extend to Hamiltonian cycles in hypercubes" over at the Open Problem Garden.
In 1993 Ruskey and Savage conjectured that in the d-dimensional hypercube, every matching M can be extended to a Hamiltonian cycle. Fink verified this for ...
A type of perfect matchings extend to hamiltonian cycles in k-ary n-cubes.
Sep 28, 2007 · Fink [F] proved Kreweras' conjecture [K] which asserts that every perfect matching of hypercube extends to a Hamiltonian cycle. Bibliography. [ ...
Feb 1, 2019 · In this paper, we prove that every perfect matching of Q n for n ≥ 4 can be extended to at least 2 2 n − 4 different hamiltonian cycles of Q n.
It has shown that any perfect matching of the hypercube Qn, n ≥ 2, can be extended to a Hamiltonian cycle [7]. As a result, we have a further result that any ...
In 1993 Ruskey and Savage conjectured that in the d-dimensional hypercube, every matching M can be extended to a Hamiltonian cycle.