On the equitable vertex arboricity of complete tripartite graphs
Zhiwei Guo, Haixing Zhao, Yaping Mao
TL;DR
This paper determines the exact strong equitable vertex 3-arboricity of complete tripartite graphs, extending previous work on bipartite graphs and generalizing equitable coloring concepts.
Contribution
It provides the exact value of the strong equitable vertex 3-arboricity for complete tripartite graphs, a previously unresolved problem.
Findings
Exact value of strong equitable vertex 3-arboricity for complete tripartite graphs
Extension of equitable coloring concepts to tripartite graphs
Generalization from bipartite to tripartite graph cases
Abstract
The equitable coloring problem, introduced by Meyer in 1973, has received considerable attention and research. Recently, Wu et al. introduced the concept of equitable (t,k)-tree-coloring, which can be viewed as a generalization of proper equitable t-coloring. The strong equitable vertex k-arboricity of complete bipartite equipartition graphs was investigated in 2013. In this paper, we study the exact value of the strong equitable vertex 3-arboricity of complete equipartition tripartite graphs.
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Taxonomy
TopicsVehicle Routing Optimization Methods · Advanced Graph Theory Research · Scheduling and Timetabling Solutions