Every planar map is four colorable

by Appel, Kenneth I.

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Title Statements

Full title :Every planar map is four colorable / Kenneth Appel, and Wolfgang Haken.

Edition Statements

Publication Date:©1989

Publication Statements

Publisher(s):American mathematical Society
Place of Publication:Providence, Rhode Island
Language:eng
Publication Date:©1989

The Physical Object

Description:1 online resource (760 pages) : : illustrations

Edition Identifiers

ISBN:9780821876862, 0821876864, 0821854313, 9780821854310
oclc:ocn882236680
LC Classification:QA612.18
Dewey Decimal:511/.5

Acknowledgments -- Introduction -- 1. History -- 2. C- and D-Reducibility -- 3. Unavoidable Sets and our Discharging Procedure -- 4. Details of the Proof -- 5. Our Checking Procedure -- Bibliography -- Part I: Discharging -- 1. Introduction D-429 -- 2. The Discharging Procedure D-435 -- 3. The Set U of Reducible Configurations D-459 -- 4. Probabilistic Considerations D-478 -- 5. Possible Improvements D-486 -- Bibliography D-489 -- Part II: Reducibility -- 1. Introduction R-491 -- 2. The Computer Programs R-492 -- 3. Immersion Reducibility R-493 -- 4. The Unavoidable Set U of Reducible Configurations R-503 -- Appendix to Part II -- (a) Planar graphs and maps -- (b) Planar graphs and triangulations -- (c) Planar graphs with contractions -- (d) Kempe components and interchanges on a colored graph -- (e) Representative colorations on a labeled n-ring Rn -- (f) Fillings/contractions of Rn -- (g) Kempe components on a maximal filling/contraction of Rn -- (h) Kempe interchangeable sets on a maximal filling/contraction -- (i) Abstract Kempe chain dispositions on Rn -- (j) Open subsets of (Nf (Bn -- (k) The Kempe related extension of a subset of (Nf (Bn -- reducibility -- (l) The outside f…