| Description |
1 online resource (760 pages) : illustrations |
| Series |
Contemporary mathematics, 0271-4132 ; volume 98 |
|
Contemporary mathematics (American Mathematical Society) ; v. 98.
|
| Contents |
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 |
| Bibliography |
Includes bibliographical references |
| Notes |
English |
|
Print version record |
| Subject |
Four-color problem.
|
|
Four-color problem
|
| Form |
Electronic book
|
| Author |
Haken, Wolfgang, author
|
| ISBN |
9780821876862 |
|
0821876864 |
|
0821854313 |
|
9780821854310 |
|
