tetcha andaj

ganitat, tetcha andaj asey sangato qee "pratyek 3-jodalelya samataliy ghan aalekhamadhye tyachya serve shirobindunmadhun (kathanvar) hamiltonian chakr asate". 25 chehare, 69 kadaa aanee 46 shirobindu asalele pratikruti udaharan tayar tayar vyaktine teey prastavit kele aanee nakarle. 21 chehare, 57 kadaa aanee 38 shirobindu asaleli anek lahan prati-udaharane nantar kiman asalyache siddha jhaale.
sambhagiy dodecahedronsarkhya bahupadimule aalekh 3-niyamit asane aavashyak aahe, joou eka bajula sahaa ansh-chaar shirobindu aanee aanee bajula aath ansh-teen shirobindu asalela dvidaleey aalekh tayar karato; kaaran konatyahi hamiltonian chakrala dvidalachya donhi bajunmadhye paryayi karave lagel, parantu tyanchyakade shirobinduchi asman sankhya aahe, sambhagiy dodecahedron hamiltonian nahee.
haah andaj mahattvapoorn hota, kaaran jarr kharaa asel tarr tyat chaar ranganche pramey soochit jhaale asateh rangchhat varnan kelyapramane, chaar ranganchi samasya hii pulvirahit ghan samtol aalekhanchya 3-dhaar-rung shodhanyachya samasyeshi samatulya aahe. hamiltonian ghan samtol aalekhamadhye, asha dhaar rung shodhane sope aaheh chakravar ekantarane done rung vapara aanee urvarit serve kadansathi tisra rung vapara. vaikalpikaritya, hamiltonian ghan samtol aalekhchya aalekhchya 4-rung thet tayar kele jaau shakatat, chakratil bahereel done rung aanee bahereel bahereel aanakhi done rung vaparoon.
tatteche prati-udaharan.
tattecha tukada.
yaa prati-udaharanachi gurukilli mhanje jyala aata tattecha tukada mhanoon olakhale jaate, jeey ujavikade dakhavale aahe.
jarr haah tukada mothya aalekhatil asel, tarr aalekhatil konatehi hamiltonian chakr varchya shirshasthani (aanee khalchyapaiki eka) aat kinwa baher jaane aavashyak aahe. too eka khalchya shirshasthani aanee aanichyyaa baher jaau shakat nahee.
ulat udaharan.
tyanantar haah tukada, hamilton nasalela tutt aalekh tayar karnyasathi, thevun vaparla jaau shakato.
chitrat dakhavalyapramane asey teen tukade ekatra qaraa. tukadyanchya "anivarya" kadaa, jyaa tukadyatoon tukadyatoon konatyahi hamiltonian margacha bhag asane aavashyak aahe, tyaa madhyavarti shirshasthani jodalelya aahet; kaaran konatehi chakr yaa teen kadanpaiki keval done kadaa vaparu shakate, hamiltonian chakr asoo shakat nahee.
parinami tayar jhalela tutt aalekh 3-jodalela aanee samtol aahe, mhanoon stenitzchya prameyanusar too polyhedroncha aalekh aahe. tyala ekoon 25 chehare, 69 kadaa aanee 46 shirobindu aahet.
tetrahedronchya teen shirobindu kapoon gunakar karoon (jyache chehare rekhachitratil chaar mothya mothya sambandhit aahet, jyapaiki teen tukadyanchya jodyanmadhil aahet aanee jyapaiki chautha bahya bhag tayar karato) jyamitiyadrushtya teey lakshat yeu shakate.
lahan prati-udaharane.
dakhavalyanusar, achookpane sahaa 38-vertex naun-hamiltonian polyhedra aahet jyat kshullak teen-bajuche cutt aahet. panchkoniy prismchya done shirobindu tattechya udaharanat vaparlya gelelya tyach tukadyane badaloon tyaa tayar kelya jaatat.
sandarbh.
anshatah vidnyanavar aadharit.biil tellarne kelelya ganitachya postingcha vapar parvangine keela jaato."

