
mikacha-ardha-oordaring

oordar sidhaanthathil oru prathyeka tharam mosham sreniye amgeekarikkaatha oru ardha-oordaring aanu bettar-kwasi-oordaring allengil bii. kyu. oo. oro mikacha-ardha-ordering nannayi ardha-oordaringaanu.
prachodanam.
nannayi-ardha-oordar" ennathu aakarshakamaaya oru aashayamaanenkilum, pala pradhana ananthamaaya pravartthanangalum nannayi-ardha-oordar cheiyunnathu samrakshikkunnilla. 
richard redo kaaranam oru udaaharanam ithu vyakthamaakkunnu. 
1965-leeii oru prabandhatthil, naash-vilyams "topological minor" bandhathinu keezhil uyaramulla marangalude klaas nannayi-kwari-oordar cheythittundennu theliyikkunnathinayi "bettar-kwari-oordaring" enna sakthamaaya ashayam roopappeduthi. athinusesham, niravadhi ardha-oordaringukal mikacha-ardha-oordaringukalaanennu theliyichukondu avaa nannayi-ardha-oordaringukalaanennu theliyikkappettittund. udaaharanathinu, chitharikkidakkunna rekheeya krama tharangalude klaas mikacha-kwari-oordar aanennu theliyichukondu richard laver laavarinte sidhaantham (munbu rolland frasseyude oru anumaanam) sthaapichu. aduthakaalathu, sariyaaya fozhsing axium prakaram, aronsajan lainukalude klaas embadability bandhathinu keezhil mikacha-kwari-oordar cheythathaanennu carlos martiness-ranero theliyichittundu.
nirvachanam.
bettar-kwari-oordaring sidhaanthathil aadya padam ozhivaakkiyukond sequence formula _ 2-naayi formula _ 1 ezhuthunnathu saadhaaranamaanu. formula 4 leeii padangalumaayi parimithamaaya, karsanamaayi vardhippikkunna seekwansukalkkaayi formula 3 ezhuthuka, formula 3 ll oru relation formula 5 inipparayunna reethiyil nirvachikkuka formula 8 undengil formula 9 formula 10, formula 11 ennivayude karsanamaaya prarambha vibhagamaanu. relation formula 5 traansitteevu allah.
oronninteyum prarambha bhagam adangiyirikkunna formula _ 3-nte ananthamaaya upavibhagamaanu oru "block" formula _ 13.
formula _ 15-nte ananthamaaya upavibhagam. oru ardha-krama formula _ 16-nuu, oru "formula _ 16-paatten" ennathu eathenkilum block formula _ 13-ll ninnu formula _ 16-lekkulla oru functionaanu. oro jody formula _ 23-num formula _ 22 aanenkil formula _ 7; allengil formula _ 25 "nallath" aanenkil oru formula _ 16-paatten formula _ 21 "mosham" ennu parayappedunnu. mosham formula 16-paatten illengil oru kwasi-oordaring formula 'bettar-kwasi-oordaring' ennu vilikkunnu.
eee nirvachanam eluppathil pravarthippikkunnathinna, naash-vilyams oru "barrier" nirvachikkunnath inclusion relation formula _ 28 prakaram jody thirichulla gadakangal thaarathamyappeduthaanaavatha oru blokkaanu. oru "formula _ 16-aarey" ennathu domaine oru barrier aaya oru formula _ 16-paatten aanu. oro blockilum oru barrier undennu nireekshikkunnathiloode, mosham formula 16-aarey illengil maathram formula 16 mikacha-kwasi-oordaring aanennu oraal kaanunnu.
simpsante badal nirvachanam.
simpson boral function formula 33-nte adisthaanathil "bettar-kwasi-oordaring" ennathinu oru badal nirvachanam avatharippichu, avide formula 34, formula 4-nte ananthamaaya upavibhaagangalude koottam, saadhaarana uthppanna topology nalkunnu.
formula _ 16" oru ardha-oordaring ayirikkatte, koodaathe vyathiriktha topologiotoppam formula _ 16 nalkuka. formula _ 4-nte chila ananthamaaya upasett formula _ 40-nuu oru boral function formulayanu "formula _ 16-array". oro formulakkum formula _ 44 aanenkil oru formula _ 16-array formula _ 25 "mosham" aanu.
formula _ 25 allaathapaksham "nallath" aanu. eee ardhathil mosham formula 16-array illengil kwasi-oordaring formula _ 16 oru "bettar-kwasi-oordaring" aanu.
pradhana sidhaanthangal.
bettar-kwari-oordaring sidhaanthathile pala pradhana phalangalum simpsante prabandhatthil inipparayunna reethiyil prathyakshappedunna minimum baad aare lemmayude anantharafalangalaanu. ettavum kuranja mosham shreni lemma aadyam prasthavikkappetta laavarinte paper kaanuka. 1965-ll naash-vilyamsinte yadhaartha prabandhatthil eee saankethikavidya undaayirunnu.
formula _ 49 oru ardhakramamaanennu karuthuka. formula 16-nte oru "paarshyal ranking" formula _ 50 ennathu formula 16-nte nannayi sthaapithamaaya bhagika kramamaanu, athaayath formula _ 53. mosham formula _ 16-arekalkku (simpson enna ardhathil) formula _ 55 umm formula _ 56 umm nirvachikkuka
formula 64 poleyulla mosham formula 16-aarey formula 25 illengil oru mosham formula 16-aarey formula 60 "minimum mosham" (paarshyal ranking formula 50 neey sambandhichidatholam) aanennu nammal parayunnu.
formula 65, formula 66 ennivayude nirvachanangal formula 16-nte bhagika ranking formula 50-neey aasrayichirikkunnu. relation formula 69 relation formula 65-nte karsanamaaya bhagamalla.
sidhaantham (minimum baad array lemma). formula _ 16 bhagika ranking ulla oru ardha-kramamayirikkatte, formula _ 25 oru mosham formula _ 16-areyaanennu karuthuka. appol oru kuranja mosham formula _ 16-aarey formula _ 60 undu, athaayath formula _ 76.