Cycles in graphs and related problems

Tom 454 / 2008

Antoni Marczyk Dissertationes Mathematicae 454 (2008), 1-98 MSC: 05C45, 05C38, 05C35. DOI: 10.4064/dm454-0-1


Our aim is to survey results in graph theory centered around four themes: hamiltonian graphs, pancyclic graphs, cycles through vertices and the cycle structure in a graph. We focus on problems related to the closure result of Bondy and Chvátal, which is a common generalization of two fundamental theorems due to Dirac and Ore. We also describe a number of proof techniques in this domain. Aside from the closure operation we give some applications of Ramsey theory in the research of cycle structure of graphs and present several methods used in the study of the structure of the set of cycle lengths in a hamiltonian graph.


  • Antoni MarczykFaculty of Applied Mathematics
    AGH University of Science and Technology
    Al. Mickiewicza 30
    30-059 Kraków, Poland

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