Cycles in graphs and related problems

Antoni Marczyk

  • 2008

Abstract

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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.

How to cite

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Antoni Marczyk. Cycles in graphs and related problems. 2008. <http://eudml.org/doc/286014>.

@book{AntoniMarczyk2008,
abstract = {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.},
author = {Antoni Marczyk},
keywords = {cycles, paths; hamiltonian graphs; traceable graphs; pancyclic graphs; toughness; claw-free graphs; closure; cyclability; pancyclability; arbitrarily vertex decomposable graphs; maximal common subgraph; cycle structure; cycle lengths; Ramsey theory},
language = {eng},
title = {Cycles in graphs and related problems},
url = {http://eudml.org/doc/286014},
year = {2008},
}

TY - BOOK
AU - Antoni Marczyk
TI - Cycles in graphs and related problems
PY - 2008
AB - 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.
LA - eng
KW - cycles, paths; hamiltonian graphs; traceable graphs; pancyclic graphs; toughness; claw-free graphs; closure; cyclability; pancyclability; arbitrarily vertex decomposable graphs; maximal common subgraph; cycle structure; cycle lengths; Ramsey theory
UR - http://eudml.org/doc/286014
ER -

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