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Damcaniaeth graffiau Hanes | Cyfeiriadau | Llywio

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Haniaeth graffiau


mathemateggwyddoniaeth gyfrifiadurolgraffiaufertigaubwyntiauymylonlinellauffwythiantLeonhard Euler1736VandermondeLeibnizCauchyL'Huillier1878Sylvesterproblem pedwar lliwFrancis Guthrie1852KempeKenneth AppelWolfgang Haken1976RobertsonSeymourSandersThomas1997genwsTaitHeawoodtopoleg18601930JordanKuratowskialgebrarheolau cylchred KirchhofftebygolrwyddErdősRényi












Damcaniaeth graffiau




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Dyluniad o graff


Mewn mathemateg a gwyddoniaeth gyfrifiadurol, astudiaeth o graffiau yw damcaniaeth graffiau. Set o fertigau, nodau neu bwyntiau wedi'u cysylltu gan ymylon, arcau neu linellau yw "graff" yn y cyd-destyn hwn, ac ni ddylid ei ddrysu gyda'r "graff" sy'n perthyn i ffwythiant.



Hanes |


Mae'n debyg mae'r papur a sgrifennwyd gan Leonhard Euler am Saith Pont Königsberg ym 1736 oedd y cyntaf a gyhoeddwyd ynglŷn â damcaniaeth graffiau. Roedd y cyhoeddiad hwn, a phapur Vandermonde am broblem y marchog yn datblygu ymhellach yr analysis situs a gychwynwyd gan Leibniz.


Ymysg y mathemategwyr enwog oedd yn weithgar ar broblemau damcaniaeth graffiau yn y canrifoedd canlynol oedd Cauchy, L'Huillier, Arthur Cayley, George Pólya, a Nicolaas Govert de Bruijn. Bathwyd y term graph (yn ein ystyr ni) ym 1878 gan Sylvester.


Un o'r problemau enwocaf yn hanes damcaniaeth graffiau yw'r problem pedwar lliw. Lluniwyd y broblem gan Francis Guthrie ym 1852 hyd a wyddys. Ni lwyddodd neb i brofi'r ddamcaniaeth am dros ganrif, er i Cayley, Kempe ac eraill cynhyrchu profion gwallus . Fe gyhoeddodd Kenneth Appel a Wolfgang Haken prawf ohonni ym 1976, ond ni argyhoeddwyd pawb yn y gymuned fathemategol ohonno, am ei fod yn ddibynnol ar defnydd o gyfrifiadur i wirio 1936 o achosion arbennig. Rhoddwyd prwawf symlach, a ystyrir yn ddilys gan bawb mwy neu lai, gan Robertson, Seymour, Sanders and Thomas ym 1997.


Roedd y broblem pedwar lliw yn ysbrydolaeth astudiaeth o lliwio graffiau ar wynebau o wahanol genws gan Tait, Heawood, Frank P. Ramsey, Hugo Hadwiger, Julius Petersen, Pál Turán ac eraill.


Bu datblygiad annibynnol topoleg rhwng 1860 a 1930 cyfranu'n ffrwythlon iawn i damcaniaeth graffiau trwy weithiau Jordan, Kuratowski a Hassler Whitney. Bu datblygiad algebra haniaethol yn ddefnyddiol hefyd, ac roedd profi rheolau cylchred Kirchhoff yn enghraifft cynnar o hynny.


Cyflwynwyd dulliau tebygolrwydd mewn damcaniaeth graffiau gan Erdős ac Rényi, a arweiniodd at astudiaeth o hap-graffiau.



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