On the P 3 -Coloring of Bipartite Graphs.

The advancement in coloring schemes of graphs is expanding over time to solve emerging problems. Recently, a new form of coloring, namely P 3 -coloring, was introduced. A simple graph is called a P 3 -colorable graph if its vertices can be colored so that all the vertices in each P 3 path of the graph have different colors; this is called the P 3 -coloring of the graph. The minimum number of colors required to form a P 3 -coloring of a graph is called the P 3 -chromatic number of the graph. The aim of this article is to determine the P 3 -chromatic number of different well-known classes of bipartite graphs such as complete bipartite graphs, tree graphs, grid graphs, and some special types of bipartite graphs. Moreover, we have also presented some algorithms to produce a P 3 -coloring of these classes with a minimum number of colors required. [ABSTRACT FROM AUTHOR]