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Antti H S Laaksonen 2017-02-28 01:40:59 +02:00
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@ -14,7 +14,7 @@ are very different.
It turns out that there is a simple rule that It turns out that there is a simple rule that
determines whether a graph contains an Eulerian path determines whether a graph contains an Eulerian path
and there is also an efficient algorithm to and there is also an efficient algorithm to
find a such path if it exists. find such a path if it exists.
On the contrary, checking the existence of a Hamiltonian path is a NP-hard On the contrary, checking the existence of a Hamiltonian path is a NP-hard
problem and no efficient algorithm is known for solving the problem. problem and no efficient algorithm is known for solving the problem.
@ -501,7 +501,7 @@ A common property in these theorems and other results is
that they guarantee the existence of a Hamiltonian that they guarantee the existence of a Hamiltonian
if the graph has \emph{a large number} of edges. if the graph has \emph{a large number} of edges.
This makes sense, because the more edges the graph contains, This makes sense, because the more edges the graph contains,
the more possibilities there is to construct a Hamiltonian graph. the more possibilities there is to construct a Hamiltonian path.
\subsubsection{Construction} \subsubsection{Construction}