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Fritsch R., Fritsch G. — The four color theorem
Fritsch R., Fritsch G. — The four color theorem



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Название: The four color theorem

Авторы: Fritsch R., Fritsch G.

Аннотация:

This elegant little book discusses a famous problem that helped to define the field now known as graph theory: what is the minimum number of colors required to print a map such that no two adjoining countries have the same color, no matter how convoluted their boundaries are. Many famous mathematicians have worked on the problem, but the proof eluded formulation until the 1970s, when it was finally cracked with a brute-force approach using a computer. The Four-Color Theorem begins by discussing the history of the problem up to the new approach given in the 1990s (by Neil Robertson, Daniel Sanders, Paul Seymour, and Robin Thomas). The book then goes into the mathematics, with a detailed discussion of how to convert the originally topological problem into a combinatorial one that is both elementary enough that anyone with a basic knowledge of geometry can follow it and also rigorous enough that a mathematician can read it with satisfaction. The authors discuss the mathematics and point to the philosophical debate that ensued when the proof was announced: just what is a mathematical proof, if it takes a computer to provide one - and is such a thing a proof at all?


Язык: en

Рубрика: Математика/Алгебра/Комбинаторика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1998

Количество страниц: 260

Добавлена в каталог: 12.03.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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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