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On the P 3 -Coloring of Bipartite Graphs

Author

Listed:
  • Zemiao Dai

    (College of Information Technology, Anhui Vocational College of Defense Technology, Luan 237011, China)

  • Muhammad Naeem

    (Department of Mathematics, COMSATS University Islamabad, Sahiwal 57000, Pakistan)

  • Zainab Shafaqat

    (Department of Mathematics, COMSATS University Islamabad, Sahiwal 57000, Pakistan)

  • Manzoor Ahmad Zahid

    (Department of Mathematics, COMSATS University Islamabad, Sahiwal 57000, Pakistan)

  • Shahid Qaisar

    (Department of Mathematics, COMSATS University Islamabad, Sahiwal 57000, Pakistan)

Abstract

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.

Suggested Citation

  • Zemiao Dai & Muhammad Naeem & Zainab Shafaqat & Manzoor Ahmad Zahid & Shahid Qaisar, 2023. "On the P 3 -Coloring of Bipartite Graphs," Mathematics, MDPI, vol. 11(16), pages 1-15, August.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:16:p:3487-:d:1215755
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