grafuri euleriene ...stleveltlevelnfc23tlevelnfcn23tleveljc0tleveljcn0t levelfollo0tlevelstartat1tlevelspace0tlevelindent0I tleveltextt01tu-3913 SItlevelnumbersStf3tchbrdrtbrdrnonetbrdrcf1 tchshdng0tchcfpat1tchcbpat1tfbias0 tfi-360tli360tjclisttabttx360 SItlistname Stlistid354580473SSIttlistoverridetableItlistoverr idetlistid354580473tlistoverridecount0tls1SSItinfoI ttitle Grafuri eulerieneSItauthor BogdanSItoperator DVDSItcreatimtyr2002tmo5tdy17tmin42SItrevtimtyr200 5tmo2tdy25thr8tmin20SItprintimtyr1998tmo10tdy18thr2 2tmin40SItversion3SItedmins1SItnofpages4SItnofords9 18SItnofchars5237SIttcompany SfinxSItnofcharss0SItvern8247SStidoctrltftnbjtaend doctnoxlattoyentexpshrtntnoultrlspctdntblnsbdbtnosp aceforulthyphcaps0tformshadethorzdoctdghspace180tdg vspace180tdghorigin1701tdgvorigin1984tdghsho0tdgvsh o0tjexpandtviekind1tviescale100tpgbrdrheadtpgbrdrfo ottnolnhtadjtbl tfet0tsectd tlinex0tendnheretsectdefaultcl Ittpnseclvl1tpnucrmtpnqctpnstart1tpnindent720tpnha ngItpntxta .SSIttpnseclvl2tpnucltrtpnqctpnstart1tpnindent720t pnhangItpntxta .SSIttpnseclvl3tpndectpnqctpnstart1tpnindent720tpn hangItpntxta .SSIttpnseclvl4tpnlcltrtpnqctpnstart1tpnindent720t pnhangItpntxta SSIttpnseclvl5tpndectpnqctpnstart1tpnindent720tpnh angItpntxtb SItpntxta SSIttpnseclvl6tpnlcltrtpnqctpnstart1tpnindent720tp nhangItpntxtb SItpntxta SSIttpnseclvl7tpnlcrmtpnqctpnstart1tpnindent720tpn hangItpntxtb SItpntxta SSIttpnseclvl8tpnlcltrtpnqctpnstart1tpnindent720tp nhangItpntxtb SItpntxta SSIttpnseclvl9tpnlcrmtpnqctpnstart1tpnindent720tpn hangItpntxtb SItpntxta SStpardtplain ts15tqc tli0tri0tidctlpartaspalphataspnumtfaautotadjustrig httrin0tlin0titap0 tf30tfs72tultlang1033tlangfe2052tcgridtlangnp1033t langfenp2052 Itf0tcf1 Grafuri eulerienetpar Stpardtplain tqc tli0tri0tidctlpartaspalphataspnumtfaautotadjustrig httrin0tlin0titap0 tfs20tlang1033tlangfe2052tcgridtlangnp1033tlangfen p2052 Itf28tfs24tultcf1 tpar Stpard tqj tfi720tli0tri0tidctlpartaspalphataspnumtfaautotadj ustrighttrin0tlin0titap0 Itf28tfs24tcf1tlang1048tlangfe2052tlangnp1048 tpar SItf307tfs24tcf1tlang1048tlangfe2052tlangnp1048 Adeseori suntem tentatfei ste3 credem simplul fapt de a traversa strte3zi sau poduri nu implicte3 nici o idee deosebitte3. Iatte3 teenste3 cte3 existte3 o celebrte3 problemte3 de traversare teen care singura idee implicatte3 este aceea de t93traversaret94, SItbtf307tfs24tcf1tlang1048tlangfe2052tlangnp1048 problema celor tbaapte poduri din Ktf6nigsbergSItf307tfs24tcf1tlang1048tlangfe2052tl angnp1048 . Aceastte3 banalte3 tbai totutbai foarte controversatte3 problemte3 a dus la aparitfeia tbai dezvoltarea teoriei grafurilor.tpar Problema se pune cam atbaatpar Stpardtplain ts16tqj tfi720tli0tri0tidctlpartaspalphataspnumtfaautotadj ustrighttrin0tlin0titap0 tf28tfs24tlang1048tlangfe2052tcgridtlangnp1048tlan gfenp2052 Itfs20tlang1024tlangfe1024tnoprooftlangnp1033tlang fenp1033 ItshpIttshpinsttshpleft3672tshptop3657tshpright511 2tshpbottom4089tshpfhdr0tshpbxcolumntshpbxignoretsh pbyparatshpbyignoretshpr1tshprk0tshpfbltxt0tshpz0ts hplid1026ItspItsn shapeTypeSItsv 202SSItspItsn fFlipHSItsv 0SSItspItsn fFlipVSItsv 0SSItspItsn lTxidSItsv 65536SSItspItsn fLineSItsv 0SSItspItsn fLayoutInCellSItsv 0SSItspItsn fLayoutInCellSItsv 0SSItshptxt tpardtplain tql tli0tri0tidctlpartaspalphataspnumtfaautotadjustrig httrin0tlin0titap0 tfs20tlang1033tlangfe2052tcgridtlangnp1033tlangfen p2052 Itf27 Figura 1.SItf27tlang1048tlangfe2052tlangnp1048 tpar SSSItshprsltIttdotdobxcolumntdobyparatdodhgt8192td ptxbxtdptxlrtbItdptxbxtexttpardtplain tql tli0tri0tidctlpartaspalphataspnumtfaautotadjustrig httrin0tlin0titap0 tfs20tlang1033tlangfe2052tcgridtlangnp1033tlangfen p2052 Itf27 Figura 1.SItf27tlang1048tlangfe2052tlangnp1048 tpar SStdpx3672tdpy3657tdpxsize1440tdpysize432tdpfillfg cr255tdpfillfgcg255tdpfillfgcb255tdpfillbgcr255tdpf illbgcg255tdpfillbgcb255tdpfillpat1tdplineholloSSSS Itf307tcf1 Oratbaul Ktf6nigsberg era atbaezat pe coasta Mte3rii Baltice, la gurile rte2ului Pregel. Pe rte2u erau doute3 insule legate de tfete3rmuri tbai teentre ele de tbaapte poduri ca teen figura 1.tpar SItf0tcf1 tpar Stpardtplain tqj tfi720tli0tri0tidctlpartaspalphataspnumtfaautotadj ustrighttrin0tlin0titap0 tfs20tlang1033tlangfe2052tcgridtlangnp1033tlangfen p2052 Itf307tfs24tcf1tlang1048tlangfe2052tlangnp1048 Oamenii care cutreierau aceste insule au observat cte3 dacte3 porneau de pe malul sudic al rte2ului, nu puteau ste3-tbai planifice plimbarea astfel teencte2t ste3 traverseze fiecare pod o singurte3 datte3. Se pte3rea cte3 ori trebuia ste3 sarte3 un pod ori ste3-l traverseze de doute3 ori.tpar tcen anul 1735 Euler a descoperit cte3 nu mai are rost ste3 se teencerce, propunte2nd urmte3toarea analizte3 a problemei, din punct de vedere matematictpar Ste3 considerte3m mai teentte2i SItitf307tfs24tcf1tlang1048tlangfe2052tlangnp1048 insula esticte3 SItf28tfs24tcf1tlang1048tlangfe2052tlangnp1048 fig.2.tpar SItf307tfs24tcf1tlang1048tlangfe2052tlangnp1048 sunt trei poduri care duc la ea. Deoarece se pleacte3 de pe malul sudic, teenseamnte3 cte3 se pleacte3 SItbtitf28tfs24tcf1tlang1048tlangfe2052tlangnp1048 din afaraSItf307tfs24tcf1tlang1048tlangfe2052tlangnp10 48 insulei estice. Deoarece fiecare din cele trei traverste3ri trebuie efectuate o singurte3 datte3, plimbarea trebuie ste3 se termine SItbtitf28tfs24tcf1tlang1048tlangfe2052tlangnp1048 peSItf307tfs24tcf1tlang1048tlangfe2052tlangnp1048 insula esticte3. tpar SItf28tfs24tcf1tlang1048tlangfe2052tlangnp1048 tpar tpar SItf307tfs24tcf1tlang1048tlangfe2052tlangnp1048 Ste3 considerte3m acum insula vesticte3tpar SItf28tfs24tcf1tlang1048tlangfe2052tlangnp1048 sunt cinci poduri care duc pe ea,SItf307tfs24tcf1tlang1048tlangfe2052tlangnp1048 iar cinci este din nou numte3r impar. Atbaadar plimbarea teencepe SItbtitf28tfs24tcf1tlang1048tlangfe2052tlangnp1048 teen afaraSItf307tfs24tcf1tlang1048tlangfe2052tlangnp10 48 insulei, tbai deci trebuie ste3 se termine SItbtitf28tfs24tcf1tlang1048tlangfe2052tlangnp1048 peSItf307tfs24tcf1tlang1048tlangfe2052tlangnp1048 insula vesticte3. tpar Stpardtplain ts16tqj tfi720tli0tri0tidctlpartaspalphataspnumtfaautotadj ustrighttrin0tlin0titap0 tf28tfs24tlang1048tlangfe2052tcgridtlangnp1048tlan gfenp2052 Itf307tcf1 Aceasta teenseamnte3 cte3 plimbarea se terminte3 teen doute3 locuri diferite simultan ceea ce e imposibiSItf0tcf1 l. tpar SItf307tcf1 Solutfeia datte3 de Euler este tipicte3 pentru personalitatea tbai ingeniozitatea sa. Tot el a scris teen anul 1736 prima lucrare de teorie a grafurilor despre problema acestor tbaapte poduri.tpar Stpardtplain tqj tfi720tli0tri0tidctlpartaspalphataspnumtfaautotadj ustrighttrin0tlin0titap0 tfs20tlang1033tlangfe2052tcgridtlangnp1033tlangfen p2052 Itf307tfs24tcf1tlang1048tlangfe2052tlangnp1048 Un ciclu al unui graf G care contfeine toate muchiile lui G se numetbate SItitf28tfs24tcf1tlang1048tlangfe2052tlangnp1048 ciclu eulerianSItf28tfs24tcf1tlang1048tlangfe2052tlangnp 1048 . UnSItf307tfs24tcf1tlang1048tlangfe2052tlangnp1048 graf G care are un ciclu eulerian se numetbate SItitf28tfs24tcf1tlang1048tlangfe2052tlangnp1048 g... Download |