04101nam 2200601 450 991078878870332120180613001225.00-8218-7686-40-8218-5431-3(CKB)3240000000069625(EBL)3112896(SSID)ssj0000712500(PQKBManifestationID)11416679(PQKBTitleCode)TC0000712500(PQKBWorkID)10645716(PQKB)10278498(MiAaPQ)EBC3112896(WaSeSS)Ind00039443(RPAM)2452639(PPN)197104215(EXLCZ)99324000000006962519890605h19891989 uy| 0engur|n|---|||||txtccrEvery planar map is four colorable /Kenneth Appel, and Wolfgang HakenProvidence, Rhode Island :American Mathematical Society,[1989]©19891 online resource (760 p.)Contemporary mathematics,0271-4132 ;volume 98Description based upon print version of record.0-8218-5103-9 Includes bibliographical references.""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 Đ?n""""(k) The Kempe related extension of a subset of Đ?n; reducibility""; ""(l) The outside filling/contraction of an immersion image""; ""(m) C-reducing a triangulation""; ""(n) The open subsets of Đ?4 and Đ?5; the critical open subsets of Đ?6""; ""(o) A. Bernhart's Bend Condition for R6-reducibility""; ""(p) The semi-critical open subsets of Đ?6 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""Contemporary mathematics (American Mathematical Society) ;v. 98.Every planar map is 4 colorableFour-color problemFour-color problem.511/.5Appel Kenneth I.1932-2013,54071Haken WolfgangMiAaPQMiAaPQMiAaPQBOOK9910788788703321Every planar map is four colorable345149UNINA