Exploring Graph Coloring Methods to Enhance Efficiency in Scheduling Issues: An Examination in the Context of Allocation and Conflict Resolution

Abstract

This paper delves into scheduling challenges within graph theory, emphasizing goals of optimization, fairness, and conflict resolution. The approach involves utilizing graph coloring, where tasks are depicted as vertices and conflicts as boundaries in a chart. The application of the Welsh-Powell algorithm is explored to lessen the requisite sum of colors. Through a case study, the paper demonstrates the utilization of graph coloring to address a scheduling issue, determining the minimum workforce required while adhering to specified constraints. Additionally, the paper discusses real-world applications of graph coloring across various domains such as regional planning, wireless communication networks, scheduling, and timetabling, underscoring its adaptability in solving optimization problems.