Equitable vertex arboricity of planar graphs
Xin Zhang

TL;DR
This paper proves that certain classes of planar graphs can be equitably partitioned into subsets inducing forests, confirming parts of a conjecture related to equitable vertex arboricity.
Contribution
It establishes equitable vertex arboricity results for specific planar graphs, advancing understanding of graph partitioning and confirming a conjecture in the field.
Findings
Partitioning of vertices into forests for graphs with independent small cycles
Results hold for all t ≥ 3
Partially confirms Wu, Zhang, and Li's conjecture
Abstract
Let be a planar graph such that all cycles of length at most 4 are independent and let be a planar graph without 3-cycles and adjacent 4-cycles. It is proved that the set of vertices of and can be equitably partitioned into subsets for every so that each subset induces a forest. These results partially confirm a conjecture of Wu, Zhang and Li.
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Taxonomy
TopicsAdvanced Graph Theory Research · Computational Geometry and Mesh Generation
