9 months ago
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Mathematics, Vol. 11, Pages 3487: On the P3-Coloring of Bipartite Graphs
Mathematics doi: 10.3390/math11163487
Authors: Zemiao Dai Muhammad Naeem Zainab Shafaqat Manzoor Ahmad Zahid Shahid Qaisar
The advancement in coloring schemes of graphs is expanding over time to solve emerging problems. Recently, a new form of coloring, namely P3-coloring, was introduced. A simple graph is called a P3-colorable graph if its vertices can be colored so that all the vertices in each P3 path of the graph have different colors; this is called the P3-coloring of the graph. The minimum number of colors required to form a P3-coloring of a graph is called the P3-chromatic number of the graph. The aim of this article is to determine the P3-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 P3-coloring of these classes with a minimum number of colors required.
