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245 10$aBranch and bound :$beine einfuhrung /$cherausgegeben von F. Weinberg
250   $a2te, geanderte Aufl
260   $aBerlin :$bSpringer-Verlag,$c1973
300   $a174 p. ;$c25 cm.
490 0 $aLecture notes in economics and mathematical systems,$x0075-8442 ;$v4
650  4$aOperations research
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100   $a19890605h19891989  uy|            0
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135   $aur|n|---|||||
181   $ctxt
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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.
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700   $aAppel$b Kenneth I.$f1932-2013,$054071
702   $aHaken$b Wolfgang
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