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Hypohamiltonian and almost hypohamiltonian graphs

Carol Zamfirescu UGent (2016)
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.
Please use this url to cite or link to this publication:
author
promoter
UGent
organization
year
type
dissertation
publication status
published
subject
pages
V, 150 pages
publisher
Ghent University. Faculty of Sciences
place of publication
Ghent, Belgium
defense location
Gent : Campus Sterre (S9, multimediazaal)
defense date
2016-05-10 09:00
ISBN
9789461973900
language
English
UGent publication?
yes
classification
D1
copyright statement
I have retained and own the full copyright for this publication
id
7213571
handle
http://hdl.handle.net/1854/LU-7213571
date created
2016-05-16 21:42:37
date last changed
2017-01-16 10:51:05
@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},
}

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.