LEADER 02200nam0 2200445 i 450 001 VIA0073059 005 20231121125925.0 010 $a8815062289 020 $aIT$b2000-12575 100 $a20040309d1999 ||||0itac50 ba 101 | $aita 102 $ait 181 1$6z01$ai $bxxxe 182 1$6z01$an 200 1 $a˜L'œItalia fascista e la Germania nazista$fAlexander J. De Grand 210 $aBologna$cIl mulino$d\1999! 215 $a159 p.$d21 cm 225 | $aUniversale paperbacks Il mulino$v348 300 $aTrad. di Maria Luisa Bassi. 410 0$1001CFI0000033$12001 $aUniversale paperbacks Il mulino$v348 500 10$aFascist Italy and nazi Germany.$3VIA0073060$9CFIV000691$915271 606 $aFascismo$xItalia$2FIR$3RMLC005356$9I 606 $aNazionalismo$xGermania$2FIR$3RMLC230121$9I 676 $a320.5330943$9$v21 700 1$aDe Grand$b, Alexander J.$3CFIV000691$4070$0139929 790 1$aDe Grand$b, Alexander$3CFIV000692$zDe Grand, Alexander J. 801 3$aIT$bIT-01$c20040309 850 $aIT-RM028 $aIT-RM0289 $aIT-RM0542 $aIT-RM0418 $aIT-RM1248 $aIT-RM0460 $aIT-FR0017 899 $aBiblioteca Universitaria Alessandrina$bRM028 899 $aBiblioteca Statale A. Baldini$bRM0289 899 $aBIBLIOTECA DEL MINISTERO DEGLI AFFARI ESTERI$bRM0542 899 $aBIBLIOTECA ACCADEMIA NAZ. DEI LINCEI E CORSINIANA$bRM0418 899 $aBiblioteca Della Fondazione Pietro Nenni$bRM1248 899 $aBiblioteca Dell' Archivio Centrale Dello Stato$bRM0460 899 $aBiblioteca umanistica Giorgio Aprea$bFR0017 $eN 912 $aVIA0073059 950 0$aBiblioteca umanistica Giorgio Aprea$d 52MAG 1/2881$e 52FLS0000230095 VMB RS $fA $h20181112$i20181112$d 52MAG 1/2881*$e 52FLS0000192715 VMB RS $fA $h20181112$i20181112$d 52MAG 1//2881**$e 52FLS0000171285 VMB RS $fA $h20181112$i20181112 977 $a 01$a 04$a 09$a 10$a 23$a 27$a 52 996 $aFascist Italy and nazi Germany$915271 997 $aUNICAS LEADER 04101nam 2200601 450 001 9910812569003321 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(RPAM)2452639 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$d©1989 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 $aFour-color problem 615 0$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 $a9910812569003321 996 $aEvery planar map is four colorable$9345149 997 $aUNINA