Decomposing planar cubic graphs
Arthur Hoffmann-Ostenhof, Tom\'a\v{s} Kaiser, Kenta Ozeki
TL;DR
This paper proves the 3-Decomposition Conjecture for connected plane cubic graphs, showing they can be decomposed into a spanning tree, a 2-regular subgraph, and a matching.
Contribution
It establishes the conjecture for a significant class of graphs, advancing understanding of graph decompositions in planar cubic graphs.
Findings
The conjecture holds for connected plane cubic graphs.
Decomposition into spanning tree, 2-regular subgraph, and matching is possible.
Supports the conjecture's validity in planar cases.
Abstract
The 3-Decomposition Conjecture states that every connected cubic graph can be decomposed into a spanning tree, a 2-regular subgraph and a matching. We show that this conjecture holds for the class of connected plane cubic graphs.
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Taxonomy
TopicsAdvanced Graph Theory Research · Computational Geometry and Mesh Generation · Advanced Materials and Mechanics