ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

Discussiones Mathematicae Graph Theory

IMPACT FACTOR 2018: 0.741

SCImago Journal Rank (SJR) 2018: 0.763

Rejection Rate (2017-2018): c. 84%

Discussiones Mathematicae Graph Theory


Discussiones Mathematicae Graph Theory 25(3) (2005) 303-310
DOI: 10.7151/dmgt.1283


David A. Pike

Department of Mathematics and Statistics
Memorial University of Newfoundland
St. John's, Newfoundland, Canada, A1C 5S7


Some bipartite Hamilton decomposable graphs that are regular of degree δ ≡ 2 (mod 4) are shown to have Hamilton decomposable line graphs. One consequence is that every bipartite Hamilton decomposable graph G with connectivity κ(G) = 2 has a Hamilton decomposable line graph L(G).

Keywords: Hamilton cycles, graph decompositions, line graphs.

2000 Mathematics Subject Classification: 05C70, 05C45.


[1] J.C. Bermond, Problem 97, Discrete Math. 71 (1988) 275, doi: 10.1016/0012-365X(88)90107-0.
[2] J.A. Bondy and U.S.R. Murty, Graph Theory with Applications (North-Holland Publishing Company, New York, 1979).
[3] K. Heinrich and H. Verrall, A Construction of a perfect set of Euler tours of K2k+1, J. Combin. Designs 5 (1997) 215-230, doi: 10.1002/(SICI)1520-6610(1997)5:3<215::AID-JCD5>3.0.CO;2-I.
[4] F. Jaeger, The 1-factorization of some line-graphs, Discrete Math. 46 (1983) 89-92, doi: 10.1016/0012-365X(83)90274-1.
[5] A. Kotzig, Z teorie konecných pravidelných grafov tretieho a stvrtého stupna, Casopis Pest. Mat. 82 (1957) 76-92.
[6] P. Martin, Cycles Hamiltoniens dans les graphes 4-réguliers 4-connexes, Aequationes Math. 14 (1976) 37-40, doi: 10.1007/BF01836203.
[7] A. Muthusamy and P. Paulraja, Hamilton cycle decompositions of line graphs and a conjecture of Bermond, J. Combin. Theory (B) 64 (1995) 1-16, doi: 10.1006/jctb.1995.1024.
[8] B.R. Myers, Hamiltonian factorization of the product of a complete graph with itself, Networks 2 (1972) 1-9, doi: 10.1002/net.3230020102.
[9] D.A. Pike, Hamilton decompositions of some line graphs, J. Graph Theory 20 (1995) 473-479, doi: 10.1002/jgt.3190200411.
[10] D.A. Pike, Hamilton decompositions of line graphs of perfectly 1-factorisable graphs of even degree, Australasian J. Combin. 12 (1995) 291-294.
[11] H. Verrall, A Construction of a perfect set of Euler tours of K2k+I, J. Combin. Designs 6 (1998) 183-211, doi: 10.1002/(SICI)1520-6610(1998)6:3<183::AID-JCD2>3.0.CO;2-B.
[12] S. Zhan, Circuits and Cycle Decompositions (Ph.D. thesis, Simon Fraser University, 1992).

Received 3 February 2004