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Every planar map is four colorable / / Kenneth Appel, and Wolfgang Haken
| Every planar map is four colorable / / Kenneth Appel, and Wolfgang Haken |
| Autore | Appel Kenneth I. <1932-2013, > |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [1989] |
| Descrizione fisica | 1 online resource (760 p.) |
| Disciplina | 511/.5 |
| Collana | Contemporary mathematics |
| Soggetto topico | Four-color problem |
| Soggetto genere / forma | Electronic books. |
| ISBN |
0-8218-7686-4
0-8218-5431-3 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""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"" |
| Altri titoli varianti | Every planar map is 4 colorable |
| Record Nr. | UNINA-9910480762403321 |
Appel Kenneth I. <1932-2013, >
|
||
| Providence, Rhode Island : , : American Mathematical Society, , [1989] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Every planar map is four colorable / / Kenneth Appel, and Wolfgang Haken
| Every planar map is four colorable / / Kenneth Appel, and Wolfgang Haken |
| Autore | Appel Kenneth I. <1932-2013, > |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [1989] |
| Descrizione fisica | 1 online resource (760 p.) |
| Disciplina | 511/.5 |
| Collana | Contemporary mathematics |
| Soggetto topico | Four-color problem |
| ISBN |
0-8218-7686-4
0-8218-5431-3 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""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"" |
| Altri titoli varianti | Every planar map is 4 colorable |
| Record Nr. | UNINA-9910788788703321 |
|
Appel Kenneth I. <1932-2013, >
|
||
| Providence, Rhode Island : , : American Mathematical Society, , [1989] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Every planar map is four colorable / / Kenneth Appel, and Wolfgang Haken
| Every planar map is four colorable / / Kenneth Appel, and Wolfgang Haken |
| Autore | Appel Kenneth I. <1932-2013, > |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [1989] |
| Descrizione fisica | 1 online resource (760 p.) |
| Disciplina | 511/.5 |
| Collana | Contemporary mathematics |
| Soggetto topico | Four-color problem |
| ISBN |
0-8218-7686-4
0-8218-5431-3 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""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"" |
| Altri titoli varianti | Every planar map is 4 colorable |
| Record Nr. | UNINA-9910812569003321 |
|
Appel Kenneth I. <1932-2013, >
|
||
| Providence, Rhode Island : , : American Mathematical Society, , [1989] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||