  In the problem of 2-coloring without monochromatic triangles (or
triangle-tree 2-coloring), vertices of the simple, connected, undirected graph
are colored with either 'black' or 'white' such that there are no 3 mutually
adjacent vertices of the same color. In this paper we are positively answering
the question posed in our previous work, namely, if there exists an algorithm
solving 2-coloring without monochromatic triangles on planar graphs with
linear-time complexity.
