Hamiltonicity of cubic Cayley graphs

Journal of the European Mathematical Society

Volumn 9, Issue 4, 2007, Pages 775-787

  Glover, Henry ^a   Marušič, Dragan ^b,c  

^a OHIO STATE UNIVERSITY   (United States)

^b UNIVERSITY OF LJUBLJANA   (Slovenia)

^c UNIVERSITY OF PRIMORSKA   (Slovenia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 36348942873     PISSN: 14359855     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (38)

1. Alspach, B.: Hamiltonian cycles in vertex-transitive graphs of order 2p. In: Proc. Tenth South-eastern Conference on Combinatorics, Graph Theory and Computing (Boca Raton, FL, 1979), Congr. Numer. XXIII-XX, Utilitas Math., Winnipeg, 131-139 (1979) Zbl 0425.05035 MR 0561039
2. Alspach, B.: The classification of hamiltonian generalized Petersen graphs. J. Combin. Theory Ser. B 34, 293-312 (1983) Zbl 0516.05034 MR 0714452
3. Alspach, B.: Lifting Hamilton cycles of quotient graphs. Discrete Math. 78, 25-36 (1989) Zbl 0702.05054 MR 1020643
4. Alspach, B.: Hamilton cycles in metacirculant graphs with prime power cardinal blocks. In: Graph Theory in Memory of G. A. Dirac (Sandbjerg, 1985), Ann. Discrete Math. 41, North-Holland, Amsterdam, 7-16 (1989) Zbl 0665.05024 MR 0975986
5. Alspach, B., Chen, C. C., McAvaney, K.: On a class of Hamiltonian laceable 3-regular graphs. Discrete Math. 151, 19-38 (1996) Zbl 0855.05078 MR 1391247
6. Alspach, B., Durnberger, E., Parsons, B.: Hamilton cycles in metacirculant graphs with prime cardinality blocks. In: Cycles in Graphs (Burnaby, 1982), Ann. Discrete Math. 27, North-Holland, Amsterdam, 27-34 (1985) Zbl 0588.05027 MR 0821504
7. Alspach, B., Locke, S., Witte, D.: The Hamilton spaces of Cayley graphs on abelian groups. Discrete Math. 82, 113-126 (1990) Zbl 0699.05036 MR 1057481
8. Alspach, B., Parsons, B.: On Hamiltonian cycles in metacirculant graphs. In: Algebraic and Geometric Combinatorics, Ann. Discrete Math. 15, North-Holland, Amsterdam, 1-7 (1982) Zbl 0493.05042 MR 0772579
9. Alspach, B., Qin, Y. S.: Hamilton-connected Cayley graphs on Hamiltonian groups. Europ. J. Combin. 22, 777-787 (2001) Zbl 0983.05050 MR 1848324
10. Alspach, B., Zhang, C. Q.: Hamilton cycles in cubic Cayley graphs on dihedral groups. Ars Combin. 28, 101-108 (1989) Zbl 0722.05047 MR 1039136
11. Biggs, N. L.: Aspects of symmetry in graphs. In: Algebraic Methods in Graph Theory, Vol. I, II (Szeged, 1978), Colloq. Math. Soc. János Bolyai 25, North-Holland, 27-35 (1981) Zbl 0485.05030 MR 0642030
12. 4. J. Combin. Theory Ser. B 72, 110-121 (1998) Zbl 0894.05038 MR 1604701
13. Cherkassof, M., Sjerve, D.: On groups generated by three involutions, two of which commute. In: The Hilton Symposium (Montreal, 1993), CRM Proc. Lecture Notes 6, Amer. Math. Soc., Providence, 169-185 (1994) Zbl 0818.20035
14. Conway, J., Sloane, N., Wilks, A.: Gray codes for reflection groups. Graphs Combin. 5, 315-325 (1989) Zbl 0684.20036 MR 1032382
15. Curran, S., Gallian, J. A.: Hamiltonian cycles and paths in Cayley graphs and digraphs - a survey. Discrete Math. 156, 1-18 (1996) Zbl 0857.05067 MR 1405010
16. Dobson, E., Gavlas, H., Morris, J., Witte, D.: Automorphism groups with cyclic commutator subgroup and Hamilton cycles. Discrete Math. 189, 69-78 (1998) Zbl 0957.05054 MR 1637709
17. Durnberger, E.: Connected Cayley graphs of semi-direct products of cyclic groups of prime order by abelian groups are hamiltonian. Discrete Math. 46, 55-68 (1983) Zbl 0521.05046 MR 0708162
18. 2(P). Discrete Math. 160, 149-163 (1996) Zbl 0864.05061 MR 1417567
19. Gould, R. J., Roth, R. L.: A recursive algorithm for Hamiltonian cycles in the (1, j, n)-Cayley graph of the alternating group. In: Graph Theory with Applications to Algorithms and Computer Science (Kalamazoo, ML, 1984), Wiley, New York, 351-369 (1985) Zbl 0578.05048 MR 0812676
20. Jaeger, F.: On vertex-induced forests in cubic graphs. In: Proc. Fifth Southeastern Conference on Combinatorics, Graph Theory and Computing (Boca Raton, FL, 1974), Congr. Numer. X, Utilitas Math., Winnipeg, 501-512 (1974) Zbl 0307.05102 MR 0357182
21. Keating, K., Witte, D.: On Hamilton cycles in Cayley graphs in groups with cyclic commutator subgroup. In: Cycles in Graphs (Burnaby, 1982), Ann. Discrete Math. 27, North-Holland, Amsterdam, 89-102 (1985) Zbl 0573.05029 MR 0821508
22. Lovász, L.: Problem 11. In: Combinatorial Structures and Their Applications (Calgary, 1969), Gordon and Breach, New York, 243-246 (1970)
23. Lübeck, F., Malle, G.: (2, 3)-generation of exceptional groups. J. London Math. Soc. 59, 109-122 (1999) Zbl 0935.20021 MR 1688493
24. Malle, G., Saxl, J., Weigel, T.: Generation of classical groups, Geom. Dedicata 49, 85-116 (1994) Zbl 0832.20029 MR 1261575
25. Marušič, D.: Hamilonian circuits in Cayley graphs. Discrete Math. 46, 49-54 (1983) Zbl 0515.05042 MR 0708161
26. k. In: Cycles in Graphs (Burnaby, 1982), Ann. Discrete Math. 27, North-Holland, Amsterdam, 115-128 (1985) Zbl 0571.05024 MR 0821510
27. 2. Discrete Math. 66, 169-174 (1987) Zbl 0626.05037 MR 0900940
28. Marušič, D.: On vertex-transitive graphs of order qp. J. Combin. Math. Combin. Comput. 4, 97-114 (1988) Zbl 0666.05040 MR 0978524
29. Marušič, D., Parsons, T. D.: Hamiltonian paths in vertex-symmetric graphs of order 5p. Discrete Math. 42, 227-242 (1982) Zbl 0501.05041 MR 0677056
30. Marušič, D., Parsons, T. D.: Hamiltonian paths in vertex-symmetric graphs of order 4p. Discrete Math. 43, 91-96 (1983) Zbl 0514.05037 MR 0680307
31. Nedela, R., Škoviera, M.: Atoms of cyclic connectivity in cubic graphs. Math. Slovaca 45, 481-499 (1995) Zbl 0844.05066 MR 1390702
32. Payan, C., Sakarovitch, M.: Ensembles cycliquement stables et graphes cubiques. Cahiers Centre Études Recherche Opér. 17, 319-343 (1975) Zbl 0314.05101 MR 0416965
33. Stein, A.: 11/2-generation of simple groups. Beiträge Algebra Geom. 39, 349-358 (1998) Zbl 0924.20027 MR 1642676
34. Tutte, W. T.: A family of cubical graphs. Proc. Cambridge Philos. Soc. 43, 459-474 (1947) Zbl 0029.42401 MR 0021678
35. Witte, D.: On Hamiltonian circuits in Cayley diagrams. Discrete Math. 38, 99-108 (1982) Zbl 0474.05036 MR 0676525
36. Witte, D.: On Hamilton cycles in Cayley graphs in groups with cyclic commutator subgroup. Discrete Math. 27, 89-102 (1985) Zbl 0573.05029 MR 0821508
37. Witte, D.: Cayley digraphs of prime-power order are Hamiltonian. J. Combin. Theory Ser. B 40, 107-112 (1986) Zbl 0558.05024 MR 0830597
38. Woldar, A.: On Hurwitz generation and genus actions of sporadic groups. Illinois J. Math. 33, 416-437 (1989) Zbl 0654.20014 MR 0996351