Graphs and Combinatorics

, Volume 34, Issue 2, pp 289–312 | Cite as

Minimal k-Connected Non-Hamiltonian Graphs

  • Guoli Ding
  • Emily Marshall
Original Paper


In this paper, we explore minimal k-connected non-Hamiltonian graphs. Graphs are said to be minimal in the context of some containment relation; we focus on subgraphs, induced subgraphs, minors, and induced minors. When \(k=2\), we discuss all minimal 2-connected non-Hamiltonian graphs for each of these four relations. When \(k=3\), we conjecture a set of minimal non-Hamiltonian graphs for the minor relation and we prove one case of this conjecture. In particular, we prove all 3-connected planar triangulations which do not contain the Herschel graph as a minor are Hamiltonian.


Hamilton cycles Graph minors 


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Copyright information

© Springer Japan KK, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Mathematics DepartmentLouisiana State UniversityBaton RougeUSA
  2. 2.Computer Science and Mathematics DepartmentArcadia UniversityGlensideUSA

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