LEADER 04105nam 2200601 450 001 9910480762403321 005 20180613001225.0 010 $a0-8218-7686-4 010 $a0-8218-5431-3 035 $a(CKB)3240000000069625 035 $a(EBL)3112896 035 $a(SSID)ssj0000712500 035 $a(PQKBManifestationID)11416679 035 $a(PQKBTitleCode)TC0000712500 035 $a(PQKBWorkID)10645716 035 $a(PQKB)10278498 035 $a(MiAaPQ)EBC3112896 035 $a(WaSeSS)Ind00039443 035 $a(PPN)197104215 035 $a(EXLCZ)993240000000069625 100 $a19890605h19891989 uy| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aEvery planar map is four colorable /$fKenneth Appel, and Wolfgang Haken 210 1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d[1989] 210 4$dİ1989 215 $a1 online resource (760 p.) 225 1 $aContemporary mathematics,$x0271-4132 ;$vvolume 98 300 $aDescription based upon print version of record. 311 $a0-8218-5103-9 320 $aIncludes bibliographical references. 327 $a""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"" 327 $a""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"" 327 $a""(j) Open subsets of ??n""""(k) The Kempe related extension of a subset of ??n; reducibility""; ""(l) The outside filling/contraction of an immersion image""; ""(m) C-reducing a triangulation""; ""(n) The open subsets of ??4 and ??5; the critical open subsets of ??6""; ""(o) A. Bernhart's Bend Condition for R6-reducibility""; ""(p) The semi-critical open subsets of ??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"" 327 $a""(t) Sufficient conditions for non-critical configurations""""(u) Conditions for non-critical reducers""; ""(v) The Z-reducible closure U* of the unavoidable set U""; ""(w) Locating reducible configurations or rings in triangulations""; ""(x) The main algorithm""; ""(y) An upper bound for the time demand, polynomial in N""; ""(z) Possible improvements""; ""Supplement to Part I""; ""Lemmas on T -dischargings, stated S-2""; ""proofs S-3""; ""Lemma (I) S-6""; ""Table l S-7""; ""Proof of Lemma (I), continued S-12""; ""Proof of Lemma (S+) S-14""; ""Proof of the qTS(V5)-Lemma Introduction S-15"" 410 0$aContemporary mathematics (American Mathematical Society) ;$vv. 98. 517 3 $aEvery planar map is 4 colorable 606 $aFour-color problem 608 $aElectronic books. 615 0$aFour-color problem. 676 $a511/.5 700 $aAppel$b Kenneth I.$f1932-2013,$054071 702 $aHaken$b Wolfgang 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910480762403321 996 $aEvery planar map is four colorable$9345149 997 $aUNINA