Factors and cycles in graphs

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F09%3A00501873" target="_blank" >RIV/49777513:23520/09:00501873 - isvavai.cz</a>

Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Factors and cycles in graphs

Popis výsledku v původním jazyce

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 ofa 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.

Název v anglickém jazyce

Factors and cycles in graphs

Popis výsledku anglicky

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 ofa 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.

Druh

O - Ostatní výsledky

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

<a href="/cs/project/1M0545" target="_blank" >1M0545: Institut Teoretické Informatiky</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2009

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů