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Fritsch R., Fritsch G. — The four color theorem |
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Предметный указатель |
- chain 145
-good 203
-compatible boundary coloring 210
-proper embedding 209
4-adic number 190
4-gon, complete 101
6—6-chain 229
A-reducible 186 208 210
Abutting blocks 195
Accessible arcwise 48
Addition modulo r 187
Adjacency matrix 192
Admissible coloring 44
Admissible n-coloring 86
Admissible vertex coloring 139
Admissible vertex coloring, (combinatorial) 142
Aigner. Martin (* 1942) 24 135 137 144 176 222
Allaire, Frank 34 186 216 217
Andorra 87
Andrews, Thomas (1813-1885) 20
Appel 24 30 33—37 37 85 148 183 192 215 216 222—223 228—230
Approach, qualitative 25
Approach, quantitative- 25
ARC 47
Arc, associated with a chain 153
Arc, joining 51
Arc, straight 51
Arcwise, accessible 48
Arnold, Wolfgang (*1930) 118
Articulation 161 219
Associated, arc 153
Associated, Jordan curve 153
Austria 59
B-reducible 186 208 213
Bacon, Francis (1560-1626) 13
Balloon 44
Baltzer, Richard (1818-1887) 21—22
Berber, Felix (1871—1930) 29
Berge, Claude 33
Bernhart, Arthur 27 34 183
Bernhart, Frank R. 34
Bigalke, Hans-Giinther (*1933) 30 186 201
Biggs, Norman L. 136
Birkhoff 25 128 153 176 184—186 210
Birkhoff diamond 156 187—214
Birkhoff number 184—185
Block 195
Block, decomposition 195
Block, selection 203
Blocks, abutting 195
Blocks, ordering of 207
Bocher, Maxime (1867-1918) 25
Bodendiek, Rainer (*1940) 61 114 144 145 150
Bolus, Harry (1834-1911) 4—5
Boole, George (1815-1864) 10
Border of a country 44 75
Border point of a country 73
Border, national, of a map 75
Border-stone 60
Borderline 46
Borderline of a country 75
Borel, Emile (1871-1956) 59
Boundary coloring 187
Boundary coloring of a configuration 190
Boundary coloring, -good - 203
Boundary coloring, -compatible - 210
Boundary coloring, essential- 188
Boundary coloring, Kempe sector of a 195
Boundary colorings, equivalent 187
Boundary of a set 49
Boundary point of a set 49
Boundary point of an arc 51
Bounded face 105
Bounded set 44
Bounding circuit of a configuration 157 161
Bounding circuit of a graph 194
Bridge 69
Buchroitner, Manfred (*1950) 11
C-reducible 186 208 214
Caratheodory. Constantin (1873-1950) 29
Cation 223
Cauchy, Augustin Louis (1789-1857) 76
Cayley 13 14 15 128
Chain 145
Chain game see Kempe chain game
Chain, 145
Chain, 6-6 229
Chain, closed- 152
Chain, Kempe 171
Chain, simple 145
Chain, simple closed 152
Chains, disjoint 145
Charge 223
Chojnacki, later Hanani, Chaim (1912-1991) 27 185 214 221 225 227
Chromodendron 194
Cigler. Johann (*1937) 109
Circuit 69
Circuit edge 69
Circuit, separating- 78
Circuit-free 69
Classes of goodness 202
Closed chain 152
Closed Jordan curve 47
Closed set 49
Closed simple-curve 47
Closed unit interval 47
Closed with respect to equivalence 192
COLOR 140 142
Color matrix 193
Color-extendible, directly- 192
Color-pair choice 194
Colored graph 171
Coloring, admissible - 44
Colorings, equivalent 86
Combinatorial graph 141
Compact set 49
Compatible, 210
Compensation 223
Complete (combinatorial) graph 141
Complete 4-gon 101
Complete graph 100
Component 64
Computing time 222
Configuration 155
Configuration, irreducible 168
Configuration, reducible- 168
Configurations, equivalent 159
Connected country 45
Connected map 64
Connected, simply- 64
continuous 47 50
Contraction 146
Contraction, geometric- 149
Contraction, simple 146
Coordinate functions 47
Core of a configuration 156
Counteredge 102
Counterexample, minimal- 86
country 62
Country, connected 45
Country, neighboring 80
Cover 195
Coxeter, Harold Scott Macdonald (*1907) 22
Criminal, minimal 86
Criminal, smallest 86
Cubic map 128
Cundy, H.Martyn 48
Curvature 223
Curve theorem, Jordan - 51
Curvilinear triangle 101
| D-irreducible 205
D-reducible 186—215
d-vertex 88
Dangling 5-couple 220
de Morgan, Augustus 5 10—11 16 104
de Morgan, Sophia (1809-1892) 11
Decomposition 195
Degree of a vertex 88 95
Degree of a vertex (combinatorial) 141
Descartes, Rend (1596-1650) 118
Dingeldey, Friedrich (1859-1939) 22
Dirac, Gabriel Andrews (Gabor) (1925-1984) 24
Discharging, L 229
Discharging, large 229
Discharging, procedure 223
Discharging, R 229
Discharging, regular 229
Discharging, S 229
Discharging, small 229
Discharging, T 229
Discharging, transversal- 229
Disjoint chains 145
Do Carmo, Manfredo P. 45
Domain, exterior, of a circuit 69
Domain, exterior, of a closed chain 153
Domain, exterior, of a closed Jordan curve 51
Domain, exterior, of a ring 153
Domain, interior, of a circuit 69
Domain, interior, of a closed chain 153
Domain, interior, of a closed Jordan curve 51
Domain, interior, of a configuration 156
Domain, interior, of a ring 153
Dual graph 118
Dual map 121
Dual regular solids 120
Dudehey, Henry Ernest 103
Duerre 27—28 30 186 190 192—194 207 222
Duerre Heesch algorithm 187
Duerre number 190
Dugundji, James (1919-1985) 49—51
EDGE 60
Edge coloring 139
Edge n-coloring 134
Edge, circuit- 69
Edge, final, of a map 69
Edge, inner, of a configuration 155
Edge, outer, of a configuration 158
Edges, multiple 99
Eisele, Carolyn 18
Elementary neighborhood 67
Ellis 10 12
Emanating point of a closed curve 52
Embed 160
Embedding, -proper- 209
Embedding, proper- 194
Empty map 68
End point of an arc 51
Equivalent boundary colorings 187
Equivalent colorings 86
Equivalent configurations 159
Errera, Alfred (1886-1960) 27 185 186
Essential boundary coloring 188
Essential obstruction 220
Euclid (around 300 B.C.) 48
Euler, Leonhard (1707-1783) 76 118
Euler, Leonhard (1707-1783), polyhedral formula 117
Exceptional face 194 208
Exterior domain of a circuit 69
Exterior domain of a closed Jordan curve 51
Exterior domain of a dosed chain 153
Exterior domain of a ring 153
Face of a graph 105 139
Face, exceptional - 208
Face, finite- 105
Face, infinite 105
Face, unbounded 105
Fary, Istvan 105 114
Fary, Istvan, Wagner and, Theorem 111
Federico, P.J. 118
Final edge 69
Final from the outset 192
Final of stage 1 202
Final of stage n + 1 205
Final vertex 69
Final, geographically 228
Finite face 105
Five-color theorem 133
Forest 69
Frame 58
France 87
Franklin, Philip (1898-1965) 25 27 184—185 210 221
Fridy, John A.(* 1937) 59
Gelbaum, Bernhard R. 48
Geographically good 228
Geometric contraction 149
Gierloff-Emden, Hans-Guenther (*1923) 11
Globe 44
Good, 203
Goodness, classes of 202
Graph 61
Graph, colored- 171
Graph, combinatorial 141
Graph, complete 100
Graph, complete, (combinatorial) 141
Graph, dual 118
Graph, line- 111
Graph, maximal plane 105
Graph, normal 151
Graph, planar 143
Graph, plane 141
Graph, saturated 105
Graph, triangulated 105
Graph, underlying combinatorial 142
Graphs, isomorphic combinatorial, 142
Graphs, Kuratowski 143
Gregory, Duncan Farquharson (1813-1844) 12
Guthrie, Francis 1—2 2
Guthrie, Frederick 5 6 6
Haendler, Wolfgang (*1920) 27
Haken 24 28—30 33—36 36 85 148 183 186 192 215 216 225 228—230
Hamilton 5 10 21 136
Hanani see Chojnacki
Harary, Frank (*1921) 61
Heawood 22 22 24 25 32 176
Heesch 27—28 28 30 32 118 168 185—186 205 216 219 221 223 227 228
Heesch 's rule of thumb 221
Heesch — Doerre-algorithm 187
Heffier, Lothar (1862-1962) 118
Heine, Eduard (1821-1881) 59
Hermite, Charles (1822-1901) 41
Heuser, Harro 48
Hilbert, David (1862-1943) 29 41
hole 44
Homeomorphic 50
Homeomorphism 50
Hopkins. Williams (1793-1866) 12
House of horrors 48
Hub 156
Infinite face 105
Initial point 51
Injectlye 47
Inner edge of a configuration 156
Inner vertex of a graph 151
Interchange see Kempe interchange
Interior domain of a circuit 69
Interior domain of a closed chain 153
Interior domain of a closed Jordan curve 51
Interior domain of a configuration 156
Interior domain of a ring 153
Interior point of a set 49
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