Barnette D. — Map Coloring Polyhedra and the Four Color Problem :: Электронная библиотека попечительского совета мехмата МГУ

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Barnette D. — Map Coloring Polyhedra and the Four Color Problem

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Название: Map Coloring Polyhedra and the Four Color Problem

Автор: Barnette D.

Аннотация:

In the summer of 1976 Kenneth Appel and Wolfgang Haken of the University of Illinois announced that they had solved the Four-Color Problem. Suddenly what had been known to several generations of mathematicians as the Four-Color Conjecture had become the Four-Color Theorem.

Since it had been a conjecture for over one hundred years that all maps are four-colorable, and since a great deal of mathematics was done in attempts to solve the Four-Color Conjecture, it will be called a conjecture rather than a theorem throughout most of this book.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 8th

Год издания: 1983

Количество страниц: 168

Добавлена в каталог: 17.04.2010

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

Предметный указатель

2-colorable maps      139 141
3-Color Theorem      134
3-connected maps      86
3-polyhedral graph      112
3-valent map      18 52
5-Color Theorem      96
Appel, K.      152ff
Arranged sums      137
Barnette, D.      62 63
Capping      68 106 111
Cauchy’s Rigidity Theorem      37
Cayley, A.      4
Chuard, J.      56
Circuit      27
Colonies      158ff
Colony pairs      158
Combinatorially regular      35
Complete graph      24
Component      41
Connected graph      25 90
Contracting edges      136
country      25
Cross cap      44
Cyclically n-connected      58
DeMorgan, A.      3ff
Descartes      22
Discharging      153 155
Duality      86ff
Eberhard, V.      117
Eberhard’s Theorem      117ff
EDGE      5 24
Edge coloring      126ff
Euler characteristic      37 43 44 50 51
Euler, L.      22
Euler’s equation      22 27 41 109
Euler’s Inequality      162
Face      25
Five-color theorem      96
Four-color theorem      152ff
Franklin, P.      152
Gardner, M.      152 154
Graph      23
Graph isomorphism      85
Grinberg      69
Grunbaum, B.      117 118
Gustin, G.      163
Guthrie, Francis      3 4
Guthrie, Frederick      3 4
Guy, R.      164
Hadwiger, H.      136
Hadwiger’s Conjecture      136ff
Haken, W.      152ff
Hamilton, Sir W.      3 55
Hamiltonian circuit      55ff 105 147 154
Handle      44
Handle body      161ff
Heawood, P.J.      5 160 161 163
Heawood’s Map      12 14
Heffter, L.      163
incident      88
Infinite maps      160
Irreducible maps      145ff
Isomorphic graphs      85ff
Isomorphic maps      78ff
Isomorphism      80ff

Kempe Chains      5ff 92
Kempe, A.B.      5ff
Kempe’s proof      5ff 28
Kirkman, T.P.      55
Kozyrev      69
Lederberg, J.      59
Leibniz      22
Loop      24
MAP      25
Mayer, J.      152 164
Moebius, A.F.      4
Moore, E.F.      151
Morgan, D.A.      50
Multiple edge      24
n-colorable      5
n-connected      65ff
Non-Hamiltonian maps      63ff
Okamura, H.      63
Ore, O.      152
Pair-coloring      158 165
Pannewitz, E.      56
Patching      13 15 18
Petersen, J.      54
Petersen’s, Graph      54 71
Planar graph      25
Polyhedral map      52
Polyhedral pair      109
Polyhedral triple      109
Polyhedron      22 31 98 108 134ff
Projective plane      42 49
Proper map      95 102
Reducible configurations      145ff
Reductions      52
Regular polyhedra      15 35ff
Reynolds, C.N.      152
Ring size      151
Ringel, G.      163ff
Simple polyhedron      34 120 123 134
Simplicial polyhedron      34 68 121 122 124
Steinitz, E.      113
Steinitz’s Theorem      113 117 123
Stempel, G.J.      152
Story, W.E.      30
Tait, P.G.      53ff 126ff
Tait’s Conjecture      52ff
Terry, C.M.      163
Topological disc      40
Torus      37ff
TREE      69
Triangular graph      146
Triangular map      65
truncating      111 113 134ff
Tutte triangle      56
Tutte, W.T.      56 67
Tutte’s map      56ff 68
Tutte’s theorem      67
Unavoidable set      153ff
Valence      5 25 158
Vertex      5 23
Vertex labelling      128ff
Wegner, G.      62
Welch, L.R.      163
Whitney, H.      65
Whitney’s theorem      65 67 73 105
Winn, C.E.      152
Youngs, J.W.T.      163

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