
thuraante ishtika factory prashnam

graph droinginte ganithashaasthrathil, thuraante ishtika factory prashnam oru samboornna ubhaykakshi graafinte droingle crossingukalude ettavum kuranja ennam aavashyappedunnu. randaam lokamahaayudhasamayathu oru ishtika faaktariyil jolie cheyyaan nirbandhithanaayappol ithu roopappeduthiya paal thuraante perilaanu eee prashnam ariyappedunnathu.
kaasimiyezhs surrankivics kandethiya oru droying reethi oro samboornna ubhaykakshi graphinum sariyaaya utharam nalkumennu anumaanikkappedunnu, ithu sariyaanenna prasthavana surrankivics crossing nambar konjekchar ennariyappedunnu. chila prathyeka kesukal maathram pariharichukondu oohaapohangal thurannirikkunnu.
uthbhavavum roopeekaranavum.
randaam lokamahaayudhasamayathu, hangarian ganithashaasthranjanaaya paal thurran oru ishtika faaktariyil jolie cheyyaan nirbandhithanaayi, choolakalil ninnu storeju cytukalilekku ishtikakal valicheriyunnu. faaktariyil oro choolayil ninnum oro sambharana sthalathekkum trackukal undaayirunnu, koodaathe trackukal parasparam kadakkunna sthalangalil vaaganukal thallaan budhimuttaayirunnu. eee tracukalkkidayilulla crossingukalude ennam kuraykkunnathinu factory engane punarroopakalppana cheyyaamennu chodikkaan thurran eee saahacharyathil ninnu prachodanam ulkkondirunnu.
ganithashaasthraparamaayi, choolakaleyum sambharana sthalangaleyum prathinidheekarikkunna, oro choolayil ninnu oro sambharana sthalathekkum traakkukale prathinidheekarikkunna, athinte arikukal ulla oru samboornna ubhaykakshi graafinte graph droying aavasyappedunnathaayi eee prashnam aupachaarikamaakkaam.
oro sheershakavum oru binduvaayi, oro arikum athinte rund anthima bindukkale bandhippikkunna oru vakramaayi, koodaathe athu aakasmikamallaatha oru attathu oru sheershakavum sthaapichittillaatha reethiyil graph thalam varaykkanam. graphile rund arikukalkk samatalam shoonyamallaatha intersection undaakumbozhellaam oru crossing kanakkakkunnu. appol chodyam ithaanu, atharamoru droingle ettavum kuranja crossingukalude ennam ethrayaanu?
eee prashnatthinte thurran roopeekaranam graafukalude crossing nambarukalekkurichulla aadya padanangalilonnaayi palappozhum amgeekarikkappedunnu.
graph droingle padanatthinte kendra lakshyamenna nilayil crossing nambarukalkku kooduthal praadhaanyam labhichu.
koodaathe vii. ell. sii. aii roopakalppanayile oru pradhana upakaranamenna nilayilum
koodaathe vyathirikthamaya jyamitiyum.
mukalile paridhi.
1952ll polandile vividha charchakalil thurran ishtika factory prashnathekkurichu samsaarikkunnath surrankievics kaasimiyezhs arbanic kandu.
crossingukalude ennathinu thulyamaaya soothravaakyangal upayogichu prashnatthinte pariharangal swathanthramaayi prasidheekarichu.
iruvarum kaanichathupole, thulyamaaya niravadhi crossingukalulla samboornna ubhaykakshi graph (oru vashath konukalum maruvashathu konukalum iruvashangaleyum bandhippikkunna arikukalumulla oru graph) varaykkaan ellaayppozhum saadhyamaan.
nirmmaanam lalithamaanu thalatthinte-akshatthil, uthbhavam ozhivaakkikkond,-akshatthinte idathuvashathum valathuvasathum thulyamo eathaandu thulyamo aaya pooyintukal sthaapikkuka.
athupole, thalatthinte-akshatthil, uthbhavam ozhivaakkikkond,-akshathinu mukalilum thazheyumaayi thulyamo eathaandu thulyamo aaya pooyintukal sthaapikkuka.
thudarnnu,-akshatthile oro pooyintineyum oru nerrekha segment upayogichu-akshatthile oro pooyintumaayi bandhippikkuka.
ennirunnaalum, eee soothravaakyam opttimal aanennathinulla avarude thelivukal, athaayath, kurachu crossingukalulla droingukal undaakilla ennathinu, thettayirunnu. prasidheekarichu pathinonnu varsham kazhiyunnathuvare, eathaandu oresamayam gerhard ringal pooll keynum eee vidavu kandethiyirunnilla.
ennirunnaalum, saraankiviksinteyum arbanikkinteyum soothravaakyam opttimal aanennu anumaanikkappedunnu. ithu surrankivics crossing nambar konjekchar ennariyappedunnu. ithinte chila prathyeka kesukal sariyaanennu ariyappedunnundengilum pothuvaaya cases ippozhum thurannukidakkunnu.
thaazhnna athirukal.
umm' umm isomorphic aayathinal, evideyaanennu pariganikkaan ithu mathiyakum. koodaathe, saraankiviksinte nirmmaanathinu krosingukalonnumilla, athu theerchayaayum mikachathaakkaan kazhiyilla. athinaal nissaaramallaattha kesukal arcum randum maathramaan.
anumaanathinte saaraankiviksinte shrama thelivu, pothuvaaya kesil asaadhuvaanengilum, kesinu anuyojyamaanu.
athinusesham ithu mattu cheria moolyangalilekku vyapippichu, oppam
surrankivics anumaanam poornnamaaya ubhaykakshi graafukalkku sariyaanennu ariyappedunnu.
eee anumaanam,,, ennivaykku sariyaanennu ariyappedunnu.
oru counderexamble nilavilundenkil, athaayath, sarankivics boundinekkaal kurachu crossingukal aavasyamulla oru graph, appol ettavum cheria counderexambilil randum vichitramaayirikkanam.
oro nischitha thiranjeduppinum, ellaavarudeyum anumaanathinte sathyam parimithamaaya ennam choisukal maathram parishodhichu parisodhikkaan kazhiyum.
kooduthal pothuve, oro samboornna ubhaykakshi graphinum niravadhi crossingukal aavasyamaanennu theliyikkappettittund, athaayath (mathiyaya valia graafukalkku) sarankivics boundu cheytha samkhyayude kuranjathu 83 shathamaanamenkilum. eee lover boundum upper boundum thammilulla vidavu adaykkunnathu oru thuranna prashnamaayi thudarunnu.
deerghachathuraakrithiyilulla crossing nambarukal.
ekapaksheeyamaaya valavukalekkaal nerrekha vibhagangalaayi arikukal varaykkendathundenkil, chila graafukalkku valanja arikukal kondu varaykkunnathinekkaal kooduthal crossingukal aavasyamaanu.
ennirunnaalum, samboornna ubhaykakshi graafukalude crossing nambarukalkkaayi surrankivics sthaapicha mukalile paridhi neraaya arikukal upayogichu maathrame nedaan kazhiyoo. athinaal, surrankivics anumaanam shariyaanenkil, poornnamaaya ubhaykakshi graafukalkku avayude crossing nambarukalkku thulyamaaya deerghachathuraakrithiyilulla crossing nambarukalundu.