diff --git a/comparable-box-dimension.tex b/comparable-box-dimension.tex
index d8a6424cd7f6193be474118b2764e39516015e36..4ed324102f928b7a51961ffb3a871d97883a7acb 100644
--- a/comparable-box-dimension.tex
+++ b/comparable-box-dimension.tex
@@ -34,7 +34,7 @@
 
 %\nolinenumbers %uncomment to disable line numbering
 
-%\hideLIPIcs  %uncomment to remove references to LIPIcs series (logo, DOI, ...), e.g. when preparing a pre-final version to be uploaded to arXiv or another public repository
+\hideLIPIcs  %uncomment to remove references to LIPIcs series (logo, DOI, ...), e.g. when preparing a pre-final version to be uploaded to arXiv or another public repository
 
 %Editor-only macros:: begin (do not touch as author)%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \EventEditors{John Q. Open and Joan R. Access}
@@ -147,7 +147,7 @@ For any graph $G$, we have $\omega(G)\le 2^{\cbdim(G)}$.
 We may assume that $G$ has bounded comparable box dimension
 witnessed by a representation $f$. To represent any clique $A = \{a_1,\ldots,a_w\}$ in $G$, the
 corresponding boxes $f(a_1),\ldots,f(a_w)$ have pairwise non-empty
-intersection.  Since axis-aligned boxes have the Helly property, there
+intersections.  Since axis-aligned boxes have the Helly property, there
 is a point $p \in \mathbb{R}^d$ contained in $f(a_1) \cap \cdots \cap
 f(a_w)$.  As each box is full-dimensional, its interior intersects at
 least one of the $2^d$ orthants at $p$. At the same time, it follows from the definition
@@ -217,7 +217,7 @@ is at most $(3^d-1)^2$. This means that when choosing the color of $v_i$ greedil
 \section{Operations}
 
 It is clear that given a touching representation of a graph $G$, one
-easily obtains a touching representation by boxes of an induced
+can easily obtains a touching representation by boxes of an induced
 subgraph $H$ of $G$ by simply deleting the boxes corresponding to the
 vertices in $V(G)\setminus V(H)$.  In this section we are going to
 consider other basic operations on graphs. In the following, to describe
@@ -1018,4 +1018,4 @@ we now alter the representation by shrinking $h(u)$ slightly away from $h(v)$ (s
 Since the hypercubes of $h$ have pairwise different sizes, the resulting touching representation of $G$ is by comparable boxes.
 \end{proof}
 
-\end{document}
+\end{document}
\ No newline at end of file