diff --git a/chapter19.tex b/chapter19.tex
index c941f15..73c3466 100644
--- a/chapter19.tex
+++ b/chapter19.tex
@@ -14,7 +14,7 @@ are very different.
 It turns out that there is a simple rule that
 determines whether a graph contains an Eulerian path
 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
 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
 if the graph has \emph{a large number} of edges.
 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}