SharedDefinitions_and_Theorems.texOpen in CoCalc
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\title{GBP---Hamiltonicity---Summer 2018}
\author{GBP}

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%\theoremstyle{plain}
\newtheorem{thm}{Theorem}
\newtheorem{prop}[thm]{Proposition}
\newtheorem{lem}[thm]{Lemma}
\newtheorem{conj}{Conjecture}
\newtheorem{cor}[thm]{Corollary}
\newtheorem{prob}[thm]{Problem}
\newtheorem{defi}[thm]{Definition}
\newtheorem{obs}{Observation}
\newtheorem{clm}{Claim}
\newtheorem{question}{Question}



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\maketitle
\begin{obs} If $G$ is a complete graph, then $G$ is Hamiltonian.\end{obs}

\begin{lem} If $G$ is a bipartite $k$-regular graph, with $k>0$ and bipartition $(X,Y)$, then $|X|=|Y|$.\end{lem}

\begin{lem} If $G$ is a bipartite, connected, $(n,k,\lambda,\mu)$-strongly-regular graph, then $G$ is a complete balanced bipartite graph.\end{lem}

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