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  • A cycle that contains every vertex of a graph is called a hamiltonian cycle and a graph which contains a hamiltonian cycle is called a hamiltonian graph. The problem of the existence of a hamiltonian cycle is closely related to the well known problem of a travelling salesman. These problems are NP-complete and NP-hard, respectively. While some necessary and sufficient conditions are known, to date, no practical characterization of hamiltonian graphs has been found. There are several ways to generalize the notion of a hamiltonian cycle. In this thesis we make original contributions in two of them, namely, k-walks and r-trestles. In particular, as our main results, we present several new sufficient conditions for the existence of k-walks and r-trestles in a graph. Furthermore we present results dealing with recognizing graphs with an r-trestle and finding them in K_{1;r}-free graphs.
  • A cycle that contains every vertex of a graph is called a hamiltonian cycle and a graph which contains a hamiltonian cycle is called a hamiltonian graph. The problem of the existence of a hamiltonian cycle is closely related to the well known problem of a travelling salesman. These problems are NP-complete and NP-hard, respectively. While some necessary and sufficient conditions are known, to date, no practical characterization of hamiltonian graphs has been found. There are several ways to generalize the notion of a hamiltonian cycle. In this thesis we make original contributions in two of them, namely, k-walks and r-trestles. In particular, as our main results, we present several new sufficient conditions for the existence of k-walks and r-trestles in a graph. Furthermore we present results dealing with recognizing graphs with an r-trestle and finding them in K_{1;r}-free graphs. (en)
Title
  • Factors and cycles in graphs
  • Factors and cycles in graphs (en)
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  • Factors and cycles in graphs
  • Factors and cycles in graphs (en)
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  • RIV/49777513:23520/09:00501873!RIV10-MSM-23520___
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  • RIV/49777513:23520/09:00501873
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  • hamiltonian cycle; walks; trestles (en)
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  • Teska, Jakub
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  • 23520
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