line*, which is placed horizontally, and sufficiently close the main line. This line contains only two vertices that forms a $K_4$ with two vertices from the main line.

5.  Beginning from one unit above and below the main line, there are uniformly distributed sensor nodes on the vertex lines.

6.  Remaining $2|F|$ horizontal lines are distributed equally above and below the main line. The ones above the main line are colored red. The rest of the horizontal lines are colored blue. All the colored lines are sufficiently far from the main line. Each $r_i$ and $b_i$ represent two mirrored copies of an edge $i$ of $H$, and we refer to them as *edge lines*. We, later on, will use the edge lines to determine the color of an edge in $H$.

7.  The Euclidean distance between each consecutive pairs of horizontal lines with the same color are equal, and greater than one unit.

8.  There exist wireless nodes on the edge lines, each neighboring exactly two sensor nodes from a vertex line, forming a triangle. These triangles are referred to as *flags*, and the vertices are referred to as *flag vertices* in the following part of the proof.

In Figure 