An update on the middle levels problem

Discrete Mathematics

Volumn 309, Issue 17, 2009, Pages 5271-5277

  Shields, Ian ^a   Shields, Brendan J ^b   Savage, Carla D ^c  

^a IBM   (United States)

^b MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^c North Carolina State University   (United States)

Author keywords

Boolean lattice; Hamilton cycles; Middle levels; Necklaces

Indexed keywords

BOOLEAN LATTICE; COMBINATORICS; HAMILTON CYCLE; HAMILTON CYCLES; HAMILTON PATH; HASSE DIAGRAMS; MIDDLE LEVELS; NECKLACES; ORDERED SET;

COMPUTATION THEORY; GRAPH THEORY; PERSONAL COMPUTERS; SET THEORY;

MEATS;

EID: 68049107259     PISSN: 0012365X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.disc.2007.11.010     Document Type: Article

References (14)

1. Babai L. Long cycles in vertex-transitive graphs. J. Graph Theory 3 3 (1979) 301-304
2. Dejter I.J. Hamilton cycles and quotients of bipartite graphs. Graph Theory with Applications to Algorithms and Computer Science (Kalamazoo, Mich., 1984) (1985), Wiley, New York 189-199
3. Duffus D., Sands B., and Woodrow R. Lexicographic matchings cannot form Hamiltonian cycles. Order 5 2 (1988) 149-161
4. Felsner S., and Trotter W.T. Colorings of diagrams of interval orders and α-sequences of sets. Discrete Math. 144 1-3 (1995) 23-31 Combinatorics of ordered sets (Oberwolfach, 1991)
5. Horák P., Kaiser T., Rosenfeld M., and Ryjáček Z. The prism over the middle-levels graph is Hamiltonian. Order 22 1 (2005) 73-81
6. Hurlbert G. The antipodal layers problem. Discrete Math. 128 1-3 (1994) 237-245
7. Johnson J.R. Long cycles in the middle two layers of the discrete cube. J. Combin. Theory Ser. A 105 2 (2004) 255-271
8. Kierstead H.A., and Trotter W.T. Explicit matchings in the middle levels of the Boolean lattice. Order 5 2 (1988) 163-171
9. Lovász L. Problem 11. Combinatorial Structures and their Applications (1970), Gorden and Breach
10. Pósa L. Hamiltonian circuits in random graphs. Discrete Math. 14 4 (1976) 359-364
11. Savage C.D. Long cycles in the middle two levels of the Boolean lattice. Ars Combin. 35 A (1993) 97-108
12. Savage C.D., and Winkler P. Monotone Gray codes and the middle levels problem. J. Combin. Theory Ser. A 70 2 (1995) 230-248
13. I.B. Shields, Hamilton cycle heuristics in hard graphs, Ph.D. Thesis, North Carolina State University, Raleigh,http://www.lib.ncsu.edu/theses/available/etd-03142004-013420/, 2004
14. I. Shields, C.D. Savage, A Hamilton path heuristic with applications to the middle two levels problem, in: Proceedings of the Thirtieth Southeastern International Conference on Combinatorics, Graph Theory, and Computing (Boca Raton, FL, 1999), vol. 140, 1999