TL;DR
This paper explores methods for constructing cubic graphs and proves a theorem about the existence of a colored disc that intersects each pair of linked edges in elementary cycles of planar cubic graphs.
Contribution
It introduces a new theorem regarding colored discs in planar cubic graphs and analyzes construction methods for such graphs.
Findings
Proved the existence of a colored disc intersecting linked edges in elementary cycles.
Provided new methods for constructing cubic graphs.
Enhanced understanding of coloring properties in planar cubic graphs.
Abstract
In this work methods of construction of cubic graphs are analyzed and a theorem of existence of a colored disc traversing each pair of linked edges belonging to an elementary cycle of a planar cubic graph is proved.
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Taxonomy
TopicsMathematics and Applications · Advanced Theoretical and Applied Studies in Material Sciences and Geometry · Computational Geometry and Mesh Generation