Graphs and Combinatorics

, Volume 32, Issue 4, pp 1329–1337 | Cite as

Hamilton Cycles in Implicit 2-Heavy Graphs

  • Junqing CaiEmail author
  • Hao Li
Original Paper


Let id(v) denote the implicit degree of a vertex v in a graph G. We define G of order n to be implicit 2-heavy if at least two of the end vertices of each induced claw have implicit degree at least \(\frac{n}{2}\). In this paper, we show that every implicit 2-heavy graph G is hamiltonian if we impose certain additional conditions on the connectivity of G or forbidden induced subgraphs. Our results extend two previous theorems of Broersma et al. (Discret Math 167–168:155–166, 1997) on the existence of Hamilton cycles in 2-heavy graphs.


Implicit degree Hamilton cycle Implicit 2-heavy 



The authors are very grateful to the anonymous referee whose helpful comments and suggestions have led to a substantially improvement of the paper.


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Copyright information

© Springer Japan 2015

Authors and Affiliations

  1. 1.School of ManagementQufu Normal UniversityRizhaoPeople’s Republic of China
  2. 2.L.R.I, UMR 8623CNRS, Université Paris-Sud 11OrsayFrance
  3. 3.Institute for Interdisciplinary ResearchJianghan UniversityWuhanPeople’s Republic of China

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