Every planar map is four colorable /

Detalles Bibliográficos
Clasificación:Libro Electrónico
Autores principales: Appel, Kenneth I., 1932-2013 (Autor), Haken, Wolfgang (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Providence, Rhode Island : American Mathematical Society, [1989]
Colección:Contemporary mathematics (American Mathematical Society) ; v. 98.
Temas:
Four-color problem.
Problème des quatre couleurs.
Four-color problem
Acceso en línea:Texto completo
Tabla de Contenidos:
  • 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 filling/contraction of an immersion image
  • (m) C-reducing a triangulation
  • (n) The open subsets of (Nf4 (B and (Nf5 (B
  • the critical open subsets of (Nf6 (B
  • (o) A. Bernhart's Bend Condition for R6-reducibility
  • (p) The semi-critical open subsets of (Nf6 (B that satisfy the Bend Condition
  • (q) R3-, R4-, R5-, and R6-reducing a triangulation
  • (r) Extended immersion images and simple extensions
  • (s) Configuration sets closed under simple extensions
  • (t) Sufficient conditions for non-critical configurations
  • (u) Conditions for non-critical reducers
  • (v) The Z-reducible closure U* of the unavoidable set U
  • (w) Locating reducible configurations or rings in triangulations.
  • (X) The main algorithm
  • (y) An upper bound for the time demand, polynomial in N
  • (z) Possible improvements
  • Supplement to Part I
  • Lemmas on T -dischargings, stated S-2
  • proofs S-3
  • Lemma (I) S-6
  • Table l S-7
  • Proof of Lemma (I), continued S-12
  • Proof of Lemma (S+) S-14
  • Proof of the qTS(V5)-Lemma Introduction S-15
  • Cases (So (B = 0,1 S-18
  • Case (So (B = 2 S-19
  • Case (So (B = 3 S-20
  • Case (So (B = 4 S-31
  • Case (So (B = 5 S-38
  • Proof of the L-Lemma S-44
  • Tables of 3- ..., 7-digit arrangements S-45
  • Proof of the qn(V1)-Lemma Case (Sn (B = 0 S-47
  • Case (Sn (B = 1 S-57
  • Case (Sn (B e"2 S-65
  • Lemmas on L- and T -dischargings stated S-66
  • Table, L2 S-68
  • Proofs S-72
  • Proof of qTL(Vk)-Lemma, k = 8, ..., 11 S-79
  • Proof of qTL(V8)-LemmaCase W e"6 S-79
  • Case W = 5 S-83
  • Case W = 4 S-93
  • Case W = 3 S-105
  • Case W = 0 S-115
  • Proof of the qTL(V9)-Lemma Case W e"6 S-121
  • Case W = 5 S-127
  • Case W = 4 S-142
  • Case W = 3 S-160
  • Case W = 0 S-167
  • Proof of the qTL(V10)-Lemma S-170
  • Case 5,L, T2 S-172
  • Case 5,L, ., L,5 S-173
  • Case (Sp (B e"8 S-174
  • Case v = 7 S-175
  • Case v = 6 or 5 S-177
  • Proof of the qTL(V11)-Lemma S-195
  • Proof of the S-Lemma S-197
  • Supplement to Part II
  • ((Sa (B) The immersion reducibility of the configurations of U S-198
  • ((Sb (B) The reducers S-202
  • ((Sd (B) The n-decreased extensions S-218
  • ((Se (B) n- and m-values and major vertices of the configurations of U S-250
  • ((Sf (B)List of configurations in U-U' S-251
  • Corresponding Class Check Lists
  • (a), (b) C-1
  • I1-1 ..., 15-35 C-1
  • C-23
  • (1a) ..., (1l) C-32
  • (2a) ..., (2fg) C-37
  • (3a) ..., (3cb) C-88
  • (4a) ..., (4g) C-125
  • CTS#04 ..., CTS#33 C-133
  • (5a) ..., (5s) C-139
  • (6a) ..., (7h) C-146
  • (8a) ..., (8c) C-152
  • (8d) ..., (8x) C-153
  • (9a) ..., (10v) C-165
  • (11a) ..., (11h) C-177
  • (12a) ..., (12g) C-179.
  • (13a) ..., (l3n) C-180
  • (14a) ..., (15c) C-185
  • (16a) ..., (16g) C-193
  • CTL#1 ..., CTL#152 C-194.

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