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Hypohamiltonian and almost hypohamiltonian graphs

(2016)
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(UGent)
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Abstract
This Dissertation is structured as follows. In Chapter 1, we give a short historical overview and define fundamental concepts. Chapter 2 contains a clear narrative of the progress made towards finding the smallest planar hypohamiltonian graph, with all of the necessary theoretical tools and techniques--especially Grinberg's Criterion. Consequences of this progress are distributed over all sections and form the leitmotif of this Dissertation. Chapter 2 also treats girth restrictions and hypohamiltonian graphs in the context of crossing numbers. Chapter 3 is a thorough discussion of the newly introduced almost hypohamiltonian graphs and their connection to hypohamiltonian graphs. Once more, the planar case plays an exceptional role. At the end of the chapter, we study almost hypotraceable graphs and Gallai's problem on longest paths. The latter leads to Chapter 4, wherein the connection between hypohamiltonicity and various problems related to longest paths and longest cycles are presented. Chapter 5 introduces and studies non-hamiltonian graphs in which every vertex-deleted subgraph is traceable, a class encompassing hypohamiltonian and hypotraceable graphs. We end with an outlook in Chapter 6, where we present a selection of open problems enriched with comments and partial results.

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Citation

Please use this url to cite or link to this publication:

Chicago
Zamfirescu, Carol. 2016. “Hypohamiltonian and Almost Hypohamiltonian Graphs”. Ghent, Belgium: Ghent University. Faculty of Sciences.
APA
Zamfirescu, C. (2016). Hypohamiltonian and almost hypohamiltonian graphs. Ghent University. Faculty of Sciences, Ghent, Belgium.
Vancouver
1.
Zamfirescu C. Hypohamiltonian and almost hypohamiltonian graphs. [Ghent, Belgium]: Ghent University. Faculty of Sciences; 2016.
MLA
Zamfirescu, Carol. “Hypohamiltonian and Almost Hypohamiltonian Graphs.” 2016 : n. pag. Print.
@phdthesis{7213571,
  abstract     = {This Dissertation is structured as follows. In Chapter 1, we give a short historical overview and define fundamental concepts. Chapter 2 contains a clear narrative of the progress made towards finding the smallest planar hypohamiltonian graph, with all of the necessary theoretical tools and techniques--especially Grinberg's Criterion. Consequences of this progress are distributed over all sections and form the leitmotif of this Dissertation. Chapter 2 also treats girth restrictions and hypohamiltonian graphs in the context of crossing numbers. Chapter 3 is a thorough discussion of the newly introduced almost hypohamiltonian graphs and their connection to hypohamiltonian graphs. Once more, the planar case plays an exceptional role. At the end of the chapter, we study almost hypotraceable graphs and Gallai's problem on longest paths. The latter leads to Chapter 4, wherein the connection between hypohamiltonicity and various problems related to longest paths and longest cycles are presented. Chapter 5 introduces and studies non-hamiltonian graphs in which every vertex-deleted subgraph is traceable, a class encompassing hypohamiltonian and hypotraceable graphs. We end with an outlook in Chapter 6, where we present a selection of open problems enriched with comments and partial results.},
  author       = {Zamfirescu, Carol},
  isbn         = {9789461973900},
  language     = {eng},
  pages        = {V, 150},
  publisher    = {Ghent University. Faculty of Sciences},
  school       = {Ghent University},
  title        = {Hypohamiltonian and almost hypohamiltonian graphs},
  year         = {2016},
}