\select@language {english}
\contentsline {part}{Jitka Novotn\'a}{4}{section*.1}
\contentsline {section}{\numberline {1}Introduction}{4}{section.1}
\contentsline {subsection}{\numberline {1.1}Motivation}{4}{subsection.1.1}
\contentsline {subsection}{\numberline {1.2}Definitions}{4}{subsection.1.2}
\contentsline {section}{\numberline {2}2-connected graphs}{5}{section.2}
\contentsline {section}{\numberline {3}Three independent spanning trees generate a 3-routing}{7}{section.3}
\contentsline {section}{\numberline {4}Reductions}{9}{section.4}
\contentsline {subsection}{\numberline {4.1}Useless edge reduction}{9}{subsection.4.1}
\contentsline {subsection}{\numberline {4.2}Nontrivial 3-cut reduction}{9}{subsection.4.2}
\contentsline {subsection}{\numberline {4.3}Odd edge reduction}{10}{subsection.4.3}
\contentsline {subsection}{\numberline {4.4}Edge near the goal reduction}{11}{subsection.4.4}
\contentsline {section}{\numberline {5}3-connected graphs have three independent spanning trees}{12}{section.5}
\contentsline {section}{\numberline {6}4-connected graphs}{15}{section.6}
\contentsline {section}{\numberline {7}Acknowledgment}{15}{section.7}