Cycles in weighted graphs and related topics

This thesis contains results on paths andcycles in graphs andon a more\ud or less relatedtopic, the vulnerability of graphs. In the first part of\ud the thesis, Chapters 2 through 5, we concentrate on paths andcycles\ud in weightedgraphs. A number of sufficient conditions are presentedfor\ud graphs to contain paths andcycles with certain properties, in particular\ud heavy (or long) paths andcycles. The secondpart of the thesis, Chapters\ud 6 and7, contains some basic results on paths andcycles in (edge-) colored\ud graphs. In the thirdpart of the thesis, Chapters 8 and9, we focus on\ud a graph parameter which can be usedto analyze the vulnerability of\ud graphs, i.e., the scattering number of graphs