153 research outputs found
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
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