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Record Nr. |
UNINA9910788788703321 |
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Autore |
Appel Kenneth I. <1932-2013, > |
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Titolo |
Every planar map is four colorable / / Kenneth Appel, and Wolfgang Haken |
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Pubbl/distr/stampa |
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Providence, Rhode Island : , : American Mathematical Society, , [1989] |
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©1989 |
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ISBN |
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0-8218-7686-4 |
0-8218-5431-3 |
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Descrizione fisica |
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1 online resource (760 p.) |
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Collana |
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Contemporary mathematics, , 0271-4132 ; ; volume 98 |
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Disciplina |
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Soggetti |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Description based upon print version of record. |
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Nota di bibliografia |
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Includes bibliographical references. |
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Nota di contenuto |
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""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. |
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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"" |
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