Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4647262 | Discrete Mathematics | 2014 | 8 Pages |
Abstract
The well-known middle levels problem is to find a Hamiltonian cycle in the graph induced from the binary Hamming graph H2(2k+1) by the words of weight k or k+1. In this paper we define the q-analog of the middle levels problem. Let n=2k+1 and let q  be a power of a prime number. Consider the set of (k+1)-dimensional subspaces and the set of k-dimensional subspaces of Fqn. Can these subspaces be ordered in a way that for any two adjacent subspaces X and Y, either XâY or YâX? A construction method which yields many Hamiltonian cycles for any given q and k=2 is presented.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Tuvi Etzion,