Version 1
: Received: 16 January 2024 / Approved: 17 January 2024 / Online: 17 January 2024 (04:25:38 CET)
How to cite:
Shukla, C.K. A Geometric and Visual Perspective on the Four Color Map Theorem and K5 Non-Planarity and Their Connection. Preprints2024, 2024011269. https://doi.org/10.20944/preprints202401.1269.v1
Shukla, C.K. A Geometric and Visual Perspective on the Four Color Map Theorem and K5 Non-Planarity and Their Connection. Preprints 2024, 2024011269. https://doi.org/10.20944/preprints202401.1269.v1
Shukla, C.K. A Geometric and Visual Perspective on the Four Color Map Theorem and K5 Non-Planarity and Their Connection. Preprints2024, 2024011269. https://doi.org/10.20944/preprints202401.1269.v1
APA Style
Shukla, C.K. (2024). A Geometric and Visual Perspective on the Four Color Map Theorem and K5 Non-Planarity and Their Connection. Preprints. https://doi.org/10.20944/preprints202401.1269.v1
Chicago/Turabian Style
Shukla, C.K. 2024 "A Geometric and Visual Perspective on the Four Color Map Theorem and K5 Non-Planarity and Their Connection" Preprints. https://doi.org/10.20944/preprints202401.1269.v1
Abstract
This paper offers a novel geometric and visual approach to the renowned Four Color Map Theorem and K5 non-planarity problem while unveiling their profound connection to the "kissing number" problem in 2D. We represent planar graphs through circles and tangents, simplifying complex structures and shedding light on these classic problems. Our proofs by contradiction, rooted in the kissing number concept, reveal that both the Four Color Map Theorem and K5 non-planarity are fundamentally linked, as they pivot around the concept of coloring. This study bridges the realms of geometry and graph theory, providing fresh insights and emphasizing the significance of the kissing number problem in various fields.
Keywords
Geometry; Graph Theory; Four Color Map Theorem; K5 Non-Planarity; Kissing Number Problem; Planar Graphs; Visual Representation; Contradiction Proofs; Coloring; Mathematical Connections
Subject
Computer Science and Mathematics, Discrete Mathematics and Combinatorics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
