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Original Articles

A characterization of graphs with supereulerian line graphs

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Pages 1-14 | Received 11 Jul 2019, Accepted 18 Dec 2019, Published online: 06 Jan 2020

References

  • A. Benhocine and J.-L. Fouquent, Pancyclic and pandconnected line graphs, J. Graph Theory 11 (1987), pp. 385–398. doi: 10.1002/jgt.3190110313
  • A. Benhocine and J.-L. Fouquent, The Chv´atal-Erdös condition for pancyclic line-graphs, Discrete Math. 66 (1987), pp. 21–26. doi: 10.1016/0012-365X(87)90115-4
  • E. van Blanken, J. van den Heuvel and H.J. Veldman, Pancyclicity of hamiltonian line graphs, Discrete Math. 138 (1995), pp. 379–385. doi: 10.1016/0012-365X(94)00220-D
  • F.T. Boesch, C. Suffel and R. Tindell, The spanning subgraphs of eulerian graphs, J. Graph Theory1 (1977), pp. 79–84. doi: 10.1002/jgt.3190010115
  • J.A. Bondy, U.S.R. Murty, Graph Theory, Springer, New York, 2008.
  • P.A. Catlin, A reduction method to find spanning Eulerian subgraphs, J. Graph Theory 12 (1988), pp. 29–44. doi: 10.1002/jgt.3190120105
  • P.A. Catlin, Supereulerian graphs: A survey, J. Graph Theory 16 (1992), pp. 177–196. doi: 10.1002/jgt.3190160209
  • P.A. Catlin, T. Iqbalunnisa, T.N. Janakiraman and N. Srinivasan, Hamilton cycles and closed trails in iterated line graphs, J. Graph Theory 14 (1990), pp. 347–364. doi: 10.1002/jgt.3190140308
  • G. Chartrand, On Hamiltonian line graphs, Trans. Am. Math. Soc. 134(3) (1968), pp. 559–566. doi: 10.1090/S0002-9947-1968-0231740-1
  • Z.-H. Chen and H.-J. Lai, Reduction techniques for super-Eulerian graphs and related topics-a survey, in Combinatorics and Graph Theory'95, Vol. 1 (Hefei), World Scientific Publishing, River Edge, NJ, 1995, pp. 53–69.
  • R. Faudree, E. Flandrin and Z. Ryjáček, Claw-free graphs, a survey, Discrete Math. 164 (1997), pp. 87–147. doi: 10.1016/S0012-365X(96)00045-3
  • F. Harary and C.St.J.A. Nash-Williams, On eulerian and hamiltoninan graphs and line graphs, Canad. Math. Bull. 8 (1965), pp. 701–709. doi: 10.4153/CMB-1965-051-3
  • R.L. Hemminger and L.W. Beineke, Line graphs and line digraphs, in Selected Topics in Graph Theory, L.W. Beineke and R.J. Wilson, eds., Academic Press, New York, 1978, pp. 271–305.
  • H.-J. Lai and Y. Shao, Problems related to hamiltonian line graphs, AMS/IP Stud. Adv. Math. 39 (2007), pp. 149–159. doi: 10.1090/amsip/039/09
  • H.-J. Lai, Y. Shao and H. Yan, An update on supereulerian graphs, WSEAS Trans. Math. 12 (2013), pp. 926–940.
  • H.-J. Lai, Y. Shao, G. Yu and M. Zhan, Hamiltonian connectedness in 3-connected line graphs, Discrete Appl. Math. 157(5) (2009), pp. 982–990. doi: 10.1016/j.dam.2008.02.005
  • H.-J. Lai, Y. Shao and M. Zhan, Every 4-connected line graph of a quasi claw-free graph is hamiltonian connected, Discrete Math. 308 (2008), pp. 5312–5316. doi: 10.1016/j.disc.2007.09.045
  • L. Lei, X. Li and B. Wang, On (s,t)-supereulerian locally connected graphs, in International Conference on Computational Science, 2007, pp. 384–388
  • L. Lei, X. Li, B. Wang and H.-J. Lai, On (s,t)-supereulerian graphs in locally highly connected graphs, Discrete Math. 310 (2010), pp. 929–934. doi: 10.1016/j.disc.2009.08.012
  • H. Li, H.-J. Lai, Y. Wu and S. Zhu, Panconnected index of graphs, Discrete Math. 340 (2017), pp. 1092–1097. doi: 10.1016/j.disc.2016.10.015
  • P. Li, K. Wang, M. Zhan and H.-J. Lai, Strongly spanning trailable graphs with short longest paths, Ars Combinatoria 137 (2018), pp. 3–39.
  • J. Liu, A. Yu, K. Wang and H.-J. Lai, Degree sum and hamiltonian-connected line graphs, Discrete Math. 341 (2018), pp. 1363–1379. doi: 10.1016/j.disc.2018.02.008
  • W.R. Pulleyblank, A note on graphs spanned by Eulerian graphs, J. Graph Theory 3 (1979), pp. 309–310. doi: 10.1002/jgt.3190030316
  • O. Veblen, An application of modular equations in analysis situs, Ann. Math. 14 (1912–1913), pp. 86–94. doi: 10.2307/1967604

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