Every Planar Map is Four ColorableAmerican Mathematical Soc., 1989 - 741 pages In this volume, the authors present their 1972 proof of the celebrated Four Color Theorem in a detailed but self-contained exposition accessible to a general mathematical audience. An emended version of the authors' proof of the theorem, the book contains the full text of the supplements and checklists, which originally appeared on microfiche. The thiry-page introduction, intended for nonspecialists, provides some historical background of the theorem and details of the authors' proof. In addition, the authors have added an appendix which treats in much greater detail the argument for situations in which reducible configurations are immersed rather than embedded in triangulations. This result leads to a proof that four coloring can be accomplished in polynomial time. |
Table des matières
1 | |
Discharging | 31 |
Reducibility | 93 |
Appendix to Part II | 171 |
Supplement to Part I | 275 |
Supplement to Part II | 475 |
Corresponding Class Check Lists | 531 |
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Expressions et termes fréquents
1-legger 5-vertex adjacency-preserving vertex-mapping adjacent algorithm arbitrary triangulation Arrangement check list attached Bend Condition Bound Lemma case-hypothesis causes an interior Class check list colorability-equivalent configuration of Figure connected components consider contains a configuration contains at least corresponding critical sub-classes D-reducible degree specifications denote discharging procedure Editors endpoints extended immersion image filling/contraction Four Color Four-Color Theorem Haken Heesch impossible by Lemma impossible since qTL induced interior overlap Kempe chain disposition Kempe components Kempe interchangeable Kempe related Kempe's L-situation Lemma 60 Lemma T2 major vertex minimal five-chromatic n-decreased extension obtained occurs open subsets Page2 planar graph planar map planar triangulation possible pre-image Proof of arl Proof of Lemma prove reducible configurations reducible ring representative coloration ring-size ringed configuration satisfies the Bend Section specified sub-case hypothesis sub-configurations supplement T-discharging Table I Page Tablel Theorem Type unavoidable set vertices of degree yields