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Fritsch R., Fritsch G. — The four color theorem |
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Предметный указатель |
Interior point of an arc 52
Interior vertex of a chain 145
Internally 6-connected 177
Irreducible configuration 168
Irreducible, D 205
Isolated vertex 61 99 140
Isomorphic combinatorial graphs 142
Italy 59 87
Joining arc 51
Jordan, Camille (1838-1922) 47
Jordan, Camille (1838-1922), closed-curve 47
Jordan, Camille (1838-1922), curve theorem 51
Jordan, Camille (1838-1922), curve, associated with a closed chain 153
Kelvin, Lord see Thomson
Kempe 15—16 17 20 22 59 118 128 131 184 185
Kempe chain 171
Kempe chain game 171 195 200 203
Kempe interchange 172 195 203
Kempe net 172 194
Kempe sector of a boundary coloring 195
Kempe sector of a colored graph 194
Klein, Felix (1849-1925) 21—22
Koch, Helge von (1870-1924) 48
Koch, John 24 35 39 186 215 216
Kummer, Ernst (1810-1893) 19
Kuratowski, Kazimierz (1896-1980) 105 144
Kuratowski, Kazimierz (1896-1980), graphs 143
Kuratowski, Kazimierz (1896-1980), theorem 144
L-discharging 229
Large discharging 229
Lebesgue, Henri (1875-1941) 27
Leg of a configuration 157
Length of a chain 145
Lexicographic ordering 187
Liechtenstein 59
Lindemann, Ferdinand yon (1852-1939) 41
Lindley, John (1799-1865) 3
Line graph 111
Line segment 51
Link of a chain 145
Lloyd, E.K. 136
Loop 99
Lorber, Patricia 5
Lyndon, Roger 38
MacKenzie, Donald (*1950) 34
Maddison, Isabel 22
Major vertex 224
MAP 60
Map, connected- 64
Map, cubic 128
Map, dual 121
Map, empty 68
Map, polygonal arc 65
Map, regular 94
Maximal plane graph 105
Maxwell, James Clerk (1831-1879) 118
May, Kenneth Ownsworth 11
Mayer 24 32 32 185 223 228 230
Memory capacity 222
Menasco, William W. 21
Miehe, Friedrich 194
Minimal counterexample 86
Minimal criminal 86
Minimal triangulation 152
Minor vertex 224
MODULO 187
Moebius, August Ferdinand (1790-1868) 21—22
Mokse, Edwin E. (*1918) ix 48 49 51 53 65
Moore, Eliakim Hastings (1863-1932) 25
Morgan see de Morgan
Multinational comer 46
Multiple edges 99
n-coloring 86
n-coloring of edges 134
n-coloring of vertices (combinatorial) 142
n-coloring, admissible 86
n-gon 52
National border of a map 75
Neighbor of a country 80
Neighbor of a vertex 145
Neighbor, secondary, of a vertex 177
Neighborhood 49
Neighborhood, elementary 67
Neighboring country 80
Neighboring vertices 145
Net see Kempe net
Neumann, Ernst (1832-1925) 19
Neutral point 61
Neutrality set 62
Newton, Isaac (1643-1727) 20
Normal graph 151
Nowhere dense 48
Obstruction 219
Obstruction, essential- 220
Olmsted, John M.H. (1911-1997) 48
Open set 49
Ordering of blocks 207
Ore, Oystein (1899—1968) viii 30 114 185
Osgood, Thomas W. (*1944) 34 186
Osgood, William Fogg (1864-1943) 48
Outer edge of a configuration 156
Outer vertex of a graph 151
Outset, good from the- 192
Parametrization 47
Pared image 28 161 167
Partition 51
Path, component 51
Path, connected 51 64
Peano, Guiseppe (1858-1939) 48
Peano, Guiseppe (1858-1939), curve 48
Peirce, Benjamin (1809-1880) 19
Peirce, Charles Sanders 15 18
Planar graph 143
Plane graph 141
Poincard, Henri (1854-1912) 26
Point boundary of a set 49
Point boundary of an arc 51
Point emanating of a closed curve 52
Point of contact 196
Point, initial, interior of a set 49
Point, initial, interior of an arc 52
Point, initial, of an arc 51
Point, neutral, of a map 61
Point, terminal, of an arc 52
Polygon 52
Polygon, star-shaped- 109
Polygonal arc, map 65
Polygonal arc, without self-intersections 52
Polyhedral formula, Euler- 117
Projection, stereographic- 45
Proper embedding 194
Qualitative approach 25
Quantitative approach 25
R-discharging 229
Recoloring 203
| rectangle 52
Rectilinear triangle 52
Reducer 181 208
Reducibility test 220
Reducible, A- 186 208 210
Reducible, B- 186 208 213
Reducible, C- 186 208 214
Reducible, configuration 168
Reducible, D- 186—205 215
Regular discharging 229
Regular map 94
Regular, dual 120
Regular, solid 117
Reichel, Hans-Christian (*1945) 109
Reynolds Jr., C.N. 27 185
Right half-open unit interval 47
Ring 153
Ring size 156
Ringel, Gerhard ( 1919) 24
Rinow, Willi (1907-1979) ix 57
Robertson, Nell 41 177 217
Rollet, A.P. 48
Rule of thumb, Heesch's 221
S-discharging 229
Saaty, Thomas L. 176 184
Saeki, Shinichi 36
San Marino 59 87
Sanders, Daniel P. 41 177 217
Saturated graph 105
Schmidt, Erhard (1876-1959) 51
Schmidt, Ulrich 36
Schneider, Ivo (*1937) 118
Schoenfiies, Arthur (1853-1928), theorem 46 53
Secondary neighbor 177
Sector see Kempe sector
Separated pairs 57
Separating circuit 78
Set of vertices 61
Seymour, Paul D. 41 177 217
Shimamoto, Yoshio (*1926) 28
Simple c1osed curve 47
Simple chain 145
Simple closed chain 152
Simple contraction 146
Simple curve 47
Simple subdivision 144
Simply connected 64
Size of a boundary coloring 187
Size of a ring 153
Size, ring 156
Small discharging 229
Smallest criminal 86
Snowflake curve 48
Sommerfeld, Arnold (1868-1951) 29
Spain 87
Spanned subgraph 156
Sparse set of edges 217
Square 52
Stage 202 205
Stanik, Rottaut 186
Star 156
Star point 109
Star-shaped 109
Stemple, J.G. 185
Stereographic projection 45
Story 15 18 18 128
Straight arc 51
Stromquist, Walter R. 34 185
Subdivision 144
Subdivision, simple- 144
Subgraph 141
Subgraph, spanned 156
Subtraction modulo r 187
Supply problem 143
Swart, Edward Reinier 34 217
Switzerland 59
Sylvester 14 15 18 19
Szele, Tibor 105
T-discharging 229
Tait 20 20 22 118 134—137 217
Terminal point 52
Thistlethwaite, Morwen B. 21
Thomas, Robin 41 177 217
Thomson, William (1824-1907) 20
Toepell, Michael (*1951) 26
Transversal discharging 229
TREE 69 199
triangle 52 69 153
Triangle, curvilinear 101
Triangle, rectilinear 52
Triangulated graph 105
Tutte, William Thomas (*1917) 25 33 34 40 137 156 199
Unavoidable set 168
Unbounded face 105
Unbounded set 44
Underlying combinatoriai graph 142
Unit circle 50
Unit disk 64
Unit interval 47
Unit interval, closed- 47
Unit interval, right haft-open - 47
United States of America 45
Valery, Paul (1871-1945) 32
Veblen, Oswald (1880-1960) 25
Vertex 61
Vertex coloring 139
Vertex coloring, (combinawrial) 142
Vertex coloring, admissible 139
Vertex coloring, admissible, (combinawrial) 142
Vertex n-coloring 139
Vertex n-coloring, (combinawrial) 142
Vertex of degree d 88
Vertex, final, of a map 69
Vertex, inner, of a graph 151
Vertex, interior, of a chain 145
Vertex, isolated- 61 99 140
Vertex, major 224
Vertex, minor 224
Vertex, neighboring 145
Vertex, outer, of a graph 151
Wagner, Klaus (*1910) 61 105 109 114 144 145 150
Wagner, Klaus (*1910) and Fary theorem 111
Weiakc, Benjamin Gotthold (1783-1836) 21—22 185
Weiakc, Benjamin Gotthold (1783-1836), Theorem 125
Weierstrass, Karl (1815-1897) 19
Weise, Karl Heinrich (1909-1990) 36
Wemicke, Paul (1866-19??) 25 167 169 224
Weyl, Hermann (1885-1955) 29
Wheel 156
Whewell 10—11 12
Whitney, Hasaler (1907-1989) 34 156 199
Wilson, R.J. 136
Winding number 51
Winn, C.E. 27 185 186
Yourigs, J.W.T. 24
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