\relax \citation{AchlioptasMolloy} \@writefile{toc}{\contentsline {section}{\tocsection {}{1}{The Algorithm and its Representation}}{1}} \@writefile{loa}{\contentsline {algocf}{\numberline {1}{\ignorespaces The Greedy Graph Coloring Algorithm}}{2}} \@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces A Representation of the Progress of the Algorithm}}{3}} \newlabel{fig:state_diagram}{{1}{3}} \@writefile{toc}{\contentsline {section}{\tocsection {}{2}{When $c<1$ the Algorithm Succeeds with High Probability}}{3}} \newlabel{sect:cless1}{{2}{3}} \@writefile{toc}{\contentsline {section}{\tocsection {}{3}{1-Stacks Stay Small Until Order $n^{1/3}$}}{3}} \newlabel{sect:onestacksmall}{{3}{3}} \citation{PollardUGMTP} \newlabel{eqn:p1t}{{3.1}{4}} \newlabel{eqn:1stacksmall}{{3.2}{4}} \@writefile{toc}{\contentsline {section}{\tocsection {}{4}{The Probability of Failure is Small Until Order $n^{2/3}$}}{4}} \newlabel{eqn:failstacksmall}{{4.1}{4}} \@writefile{toc}{\contentsline {section}{\tocsection {}{5}{An Upper Bound on the Maximum $S_2(t)$}}{4}} \newlabel{eqn:s2upper}{{5.1}{4}} \newlabel{eqn:bennet}{{5.2}{4}} \@writefile{toc}{\contentsline {section}{\tocsection {}{6}{Clearing out 1-Stacks}}{5}} \newlabel{eqn:s1bound}{{6}{6}} \newlabel{eqn:probn}{{6.1}{6}} \newlabel{eqn:nbound}{{6.2}{6}} \@writefile{toc}{\contentsline {section}{\tocsection {}{7}{A Summary and Justification for Subsequent Sections}}{6}} \bibstyle{chicago} \bibdata{DBP} \bibcite{AchlioptasMolloy}{\citeauthoryear {Achlioptas and Molloy}{Achlioptas and Molloy}{1997}} \bibcite{PollardUGMTP}{\citeauthoryear {Pollard}{Pollard}{2001}} \newlabel{tocindent-1}{0pt} \newlabel{tocindent0}{15.0pt} \newlabel{tocindent1}{21.0pt} \newlabel{tocindent2}{0pt} \newlabel{tocindent3}{0pt} \@writefile{toc}{\contentsline {section}{\tocsection {}{}{References\begingroup \@temptokena {{\uppercase {References}}{\uppercase {References}}}\xdef {\uppercase {References}}{\uppercase {References}}{}\mark {}\endgroup }}{7}}