Maximal Planar Graph Theory and the Four-Color Conjecture

This open access book integrates foundational principles with advanced methodologies concerning maximal planar graphs. It offers readers an exceptional examination of graph structures, chromatic polynomials, and the construction and proof techniques of the Four-Color Conjecture. It is tailored for r...

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Main Author: Xu, Jin
Format: Online
Language:English
Published: Springer Nature 2025
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Online Access:ONIX_20250613T105552_9789819647453_39
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author Xu, Jin
author_browse Xu, Jin
author_facet Xu, Jin
author_sort Xu, Jin
collection Directory of Open Access Books
description This open access book integrates foundational principles with advanced methodologies concerning maximal planar graphs. It offers readers an exceptional examination of graph structures, chromatic polynomials, and the construction and proof techniques of the Four-Color Conjecture. It is tailored for researchers, educators, and students involved in graph theory, combinatorics, and computational mathematics. The book consists of nine meticulously developed chapters. It starts with fundamental concepts in graph theory and then advances to pioneering computational proofs and recursive formulas of the chromatic number related to maximal planar graphs. Notable features include comprehensive discharging techniques, innovative approaches for constructing graphs of various orders, and groundbreaking conjectures concerning tree-colorability and unique four-colorability. The concluding chapter introduces Kempe's changes, offering new insights into the dynamics of graph coloring. Whether you are an academic enhancing your theoretical knowledge or a student searching for clear explanations for complex concepts, this book provides essential tools for navigating and addressing some of the most intricate challenges in graph theory. Its rigorous analysis and computational techniques equip readers with the necessary skills to engage deeply with maximal planar graph problems, making it an indispensable resource for advancing research and practical applications. No prior knowledge is necessary; however, a foundational understanding of graph theory is advised. This opportunity presents a chance to explore innovative perspectives and methodologies that expand the horizons of mathematical inquiry and proof development.
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language eng
publishDate 2025
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spelling doab-20.500.12854ir-1613622025-06-14T05:07:29Z Maximal Planar Graph Theory and the Four-Color Conjecture Xu, Jin Graph Theory Planar Graphs Chromatic Polynomial Maximal Planar Graph Four Color Conjecture Discharging Proof Techniques Graph Isomorphism Algorithms Recursive Graph Construction thema EDItEUR::U Computing and Information Technology::UY Computer science::UYA Mathematical theory of computation This open access book integrates foundational principles with advanced methodologies concerning maximal planar graphs. It offers readers an exceptional examination of graph structures, chromatic polynomials, and the construction and proof techniques of the Four-Color Conjecture. It is tailored for researchers, educators, and students involved in graph theory, combinatorics, and computational mathematics. The book consists of nine meticulously developed chapters. It starts with fundamental concepts in graph theory and then advances to pioneering computational proofs and recursive formulas of the chromatic number related to maximal planar graphs. Notable features include comprehensive discharging techniques, innovative approaches for constructing graphs of various orders, and groundbreaking conjectures concerning tree-colorability and unique four-colorability. The concluding chapter introduces Kempe's changes, offering new insights into the dynamics of graph coloring. Whether you are an academic enhancing your theoretical knowledge or a student searching for clear explanations for complex concepts, this book provides essential tools for navigating and addressing some of the most intricate challenges in graph theory. Its rigorous analysis and computational techniques equip readers with the necessary skills to engage deeply with maximal planar graph problems, making it an indispensable resource for advancing research and practical applications. No prior knowledge is necessary; however, a foundational understanding of graph theory is advised. This opportunity presents a chance to explore innovative perspectives and methodologies that expand the horizons of mathematical inquiry and proof development. 2025-06-14T05:07:28Z 2025-06-14T05:07:28Z 2025-06-13T09:21:25Z 2025 book ONIX_20250613T105552_9789819647453_39 https://library.oapen.org/handle/20.500.12657/103595 9789819647453 9789819647446 https://directory.doabooks.org/handle/20.500.12854/161362 eng open access image/jpeg n/a https://library.oapen.org/bitstream/20.500.12657/103595/1/9789819647453.pdf Springer Nature Springer Nature Singapore 10.1007/978-981-96-4745-3 10.1007/978-981-96-4745-3 9fa3421d-f917-4153-b9ab-fc337c396b5a 9789819647453 9789819647446 Springer Nature Singapore 232 Singapore open access
spellingShingle Graph Theory
Planar Graphs
Chromatic Polynomial
Maximal Planar Graph
Four Color Conjecture
Discharging Proof Techniques
Graph Isomorphism Algorithms
Recursive Graph Construction
thema EDItEUR::U Computing and Information Technology::UY Computer science::UYA Mathematical theory of computation
Xu, Jin
Maximal Planar Graph Theory and the Four-Color Conjecture
title Maximal Planar Graph Theory and the Four-Color Conjecture
title_full Maximal Planar Graph Theory and the Four-Color Conjecture
title_fullStr Maximal Planar Graph Theory and the Four-Color Conjecture
title_full_unstemmed Maximal Planar Graph Theory and the Four-Color Conjecture
title_short Maximal Planar Graph Theory and the Four-Color Conjecture
title_sort maximal planar graph theory and the four color conjecture
topic Graph Theory
Planar Graphs
Chromatic Polynomial
Maximal Planar Graph
Four Color Conjecture
Discharging Proof Techniques
Graph Isomorphism Algorithms
Recursive Graph Construction
thema EDItEUR::U Computing and Information Technology::UY Computer science::UYA Mathematical theory of computation
topic_facet Graph Theory
Planar Graphs
Chromatic Polynomial
Maximal Planar Graph
Four Color Conjecture
Discharging Proof Techniques
Graph Isomorphism Algorithms
Recursive Graph Construction
thema EDItEUR::U Computing and Information Technology::UY Computer science::UYA Mathematical theory of computation
url ONIX_20250613T105552_9789819647453_39
work_keys_str_mv AT xujin maximalplanargraphtheoryandthefourcolorconjecture