Schack och matematik

INNEHÅLLSFÖRTECKNING
1 INLEDNING............................................................................................................................................................................... 4
1.1 SCHACKETS HISTORIA .......................................................................................................................................................4
1.2 MATEMATIKER INTRESSERAR SIG FÖR SCHACK.............................................................................................................4
1.3 NÅGRA KÄNDA PROBLEM .................................................................................................................................................5
1.3.1 Åtta damer.................................................................................................................................................................... 5
1.3.2 Icke-attackerande torn ............................................................................................................................................... 6
1.3.3 Minimalt och maximalt antal kungar...................................................................................................................... 7
2 INTRODUKTION TILL SPRINGARCYKEL/TUR...................................................................................................... 9
2.1 VAD ÄR SPRINGARCYKEL/TUR? .......................................................................................................................................9
2.2 BAKGRUND..........................................................................................................................................................................9
3 GRAFTEORI...........................................................................................................................................................................11
3.1 GRUNDLÄGGANDE BEGREPP INOM GRAFTEORI ...........................................................................................................12
3.2 BIPARTIT GRAF .................................................................................................................................................................13
3.3 EULERSKA GRAFER..........................................................................................................................................................14
3.4 HAMILTONSKA GRAFER..................................................................................................................................................15
4 MATEMATISK BESKRIVNING PÅ SPRINGARPROBLEMET...........................................................................16
4.1 TILLÄMPNING AV WARNSDORFFS METOD....................................................................................................................17
4.2 FINNS DET NÅGRA GENERELLA REGLER FÖR EN SPRINGARCYKEL?..........................................................................21
4.3 GÅR DET ATT RÄKNA ALLA SPRINGARCYKLER FÖR ETT N X M BRÄDE?...................................................................22
4.4 CLIQUE OCH COCLIQUES.................................................................................................................................................23
5 SAMMANFATTNING..........................................................................................................................................................25
6 REFERENSER.........................................................................................................................................................................27
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