LEADER 03737nam 22004815 450 001 9911003576803321 005 20250523130242.0 010 $a981-9647-45-2 024 7 $a10.1007/978-981-96-4745-3 035 $a(CKB)39124518000041 035 $a(DE-He213)978-981-96-4745-3 035 $a(MiAaPQ)EBC32154287 035 $a(Au-PeEL)EBL32154287 035 $a(OCoLC)1524421980 035 $a(EXLCZ)9939124518000041 100 $a20250523d2025 u| 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aMaximal Planar Graph Theory and the Four-Color Conjecture /$fby Jin Xu 205 $a1st ed. 2025. 210 1$aSingapore :$cSpringer Nature Singapore :$cImprint: Springer,$d2025. 215 $a1 online resource (XIV, 232 p. 179 illus., 8 illus. in color.) 311 08$a981-9647-44-4 327 $aChapter 1 Graph Theory Fundamentals -- Chapter 2 Discharging and Structure of Maximal Planar Graphs -- Chapter 3 Computer-Based Proofs of Four Color Conjecture -- Chapter 4 Construction of Maximal Planar Graphs with the same order -- Chapter 5 Construction of Maximal Planar Graphs with the different order -- Chapter 6 Generating System of Maximal Planar Graphs -- Chapter 7 Recursion Formulae of Chromatic Polynomial and Four-Color Conjecture -- Chapter 8 Purely Tree-colorable and Uniquely 4-Colorable Maximal Planar Graph Conjectures -- Chapter 9 Kempe Change. 330 $aThis 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. 606 $aComputer science 606 $aGeometry 606 $aComputational Geometry 615 0$aComputer science. 615 0$aGeometry. 615 14$aComputational Geometry. 676 $a004.0151 700 $aXu$b Jin$4aut$4http://id.loc.gov/vocabulary/relators/aut$01784601 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9911003576803321 996 $aMaximal Planar Graph Theory and the Four-Color Conjecture$94384517 997 $aUNINA