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V@GAOUI@G I@REVC VEH@[C B@G JUGA[C

@. I@RVCO[ B@G BEJCGC[C VEH@[C 0. I`trcos 

I`trcos `b`h`n susug`g so`h`r eheieg-eheieg b`h`i fegtuo f`rcs b`g omhmi.

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I`trcos feruour`g < f`rcs x omhmi `t`u (i x g)

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Fefer`p` legcs i`trcos onusus < 0) I`trcos fulur s`gao`r F`rcs b`g omhmigy` s`i`. 6) I`trcos scietrc `cl 9 ` lc ugtuo setc`p c b`g b`g l  l ;) I`trcos fcger `t`u i`trcos zerm-mge [etc`p eheieggy` n`gy` fergch`c 4 `t`u0. 2) I`trcos tr`gspmse Ruo`r f`rcs b`g omhmi 5) I`trcos bc`amg`h I`trcos fulur s`gao`r bega`g `cl 9 4 ugtuo c ≤ l :) I`trcos cbegtct`s I`trcos bc`amg`h bega`g seiu` eheieg bc`amg`h 9 0 1) I`trcos seactca` f`w`n `t`u `t`s

6. Veh`sc 

Veh`sc `b`h`n nufuga`g `gt`r` eheieg s`tu ncipug`g bega`g eheieg ncipug`g h`cg.

 

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Veh`sc fcger V `gt`r` ncipug`g @ b`g F Ncipug`g f`ac`g b`rc pero`hc`g k`rtesc`g b`rc ncipug`g @ b`g F V ⊊ (@ Ñ F)

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Veh`sc onusus p`b` 0 ncipug`g Veh`sc V `b`h`n ncipug`g f`ac`g b`rc pero`hc`g k`rtesc`g `gt`r` ncipug`g ctu segbcrc V ⊊ (@ Ñ @)

F. VETVE[EGR@[C VEH@[C 0. Bc`ar`i T`g`n Lco` p`s`ga`g p`s`ga`g eheieg @ b`g F `b`h`n eheieg eheieg b`rc reh`sc V, a`if`ro`g p`g`n b`rc eheieg @ oe eheieg F y`ga iegy`t`o`g @ fereh`sc bega`g F.

6. R`feh Omhmi pert`i` iegy`t`o`g b`er`n `s`h (bmi`cg (bmi`cg)) b`g omhmi oebu` iegy`t`o`g b`er`n n`sch.

 

;. I`trcos I`trcos ugtuo ierepresegt`sco`g reh`sc ierup`o`g i`trcos fcger `t`u zerm-mge `t`u  zerm-mge..

2. Ar`j fer`r`n (reh`sc p`b` s`tu ncipug`g) Rc`p eheieg ncipug`g bcgy`t`o`g bega`g tctco bcsefut lua` scipuh `t`u vertex vertex.. Rc Rc`p `p p` p`s` s`ga ga`g `g teru teruru rutt y` y`ga ga iegy iegy`t `t`o `o`g `g re reh` h`sc sc bc bcgy` gy`t` t`o`g o`g bega` bega`g g fusur fusur y`ga y`ga `r `r`ng `ngy` y` bctugluoo`g bega`g p`g`n.

 

K. [CJ@R-[CJ@R VEH@[C 0. Vejheoscj (rejhexcve (rejhexcve)) 

[etc`p eheieg p`b` ncipug`g @ fernufuga`g bega`g bcrcgy` segbcrc.

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Bcsefut rejheoscj  lco` (`, (`, `) `) ∌ V ugtuo setc`p ` ∌ @

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Bcsefut tcb`o

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Kmgtmn < reh`sc ‘ n`fcs ieif`ac ’ p`b` ncipug`g fch`ga`g fuh`t pmsctcj 

rejheoscj lco`

terb`p`t ` ∌ @ sebeicoc`g sencgaa` (`,`) ∃ V 

6. Iegan`gt`r (tr`gsctcve (tr`gsctcve)) 

Veh`sc V p`b` ncipug`g @ bcsefut iegan`gt`r lco` < (`,f `,f)) ∌ V ∡ (f,k ) ∌ V, ugtuo seiu` `,f,k ∌   @ @

;. [et`gaoup ( syiietrck)  syiietrck) b`g Rmh`o-[et`gaoup (`gtcsyiietrck (`gtcsyiietrck)) 

Veh`sc V p`b` ncipug`g @ bcsefut set`gaoup lco` <

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Veh`sc V p`b` ncipug`g @ tcb`o set`gaoup lco` <

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Veh`sc V p`b` ncipug`g @ bcsefut tmh`o-set`gaoup lco` <

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Veh`sc V p`b` ncipug`g @ tcb`o tmh`o-set`gaoup lco` <

 

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Vepresegt`sc I`trcos `) reh`sc y`ga set`gaoup ieichcoc i`trcos y`ga eheieg-eheieg bc f`w`n bc`amg`h ut`i` ierup`o`g pegkericg`g eheieg-eheieg bc `t`s bc`amg`h ut`i`.

 f) ar`j fer`r`n reh`sc set`gaoup bckcrco`g mhen fusur ` oe f ↖ fusur f oe ` k) i`trcos reh`sc y`ga tmh`o-set`gaoup `b`h`n lco` s`h`n s`tu i cl 9 4 `t`u i lc 9 4, fch` c ≤ l

b) ar`j fer`r`n reh`sc tmh`o-set`gaoup bckcrco`g bega`g tcb`o `b`gy` 6 fusur `r`n ferh`w`g`g

B. VEH@[C CGZEV[C, OMIFCG@[C, B@G OMITM[C[C VEH@[C 0. Veh`sc Cgversc

Kmgtmn <  V < ` `b`h`n `y`n b`rc f ↖ V ↖ V-0 9 f `b`h`n `g`o b`rc `

 

6. Iegaomifcg`sc Veh`sc Veh`sc fcger `b`h`n ncipug`g p`s`ga`g terurut i`o` mper`sc ncipug`g h`cggy` lua` ferh`ou.

;. Omipmscsc Veh`sc 

Bejcgcsc omipmscsc 6 fu`n reh`sc < 

V reh`sc b`rc @ oe F

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[ reh`sc b`rc F oe K Omip Om ipms mscs cscc V b` b`g g [, bcgy bcgy`t `t`o `o`g `g be bega ga`g `g [ m V ? `b `b`h `h`n `n re reh` h`sc sc b` b`rc rc @ oe K, y` y`ga ga

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bcbejcgcsco`g mhen p`s`ga`g eheieg @-K sebeicoc`g

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Kmgtmn < 

@ 9 {0,6,;}

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F 9 {6,2,:,>}

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K 9 {s,t,u}

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Veh`sc V iegaa`if`ro`g nufuga`g eheieg ncipug`g @ bega`g ncipug`g F

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Veh`sc [ iegy`t`o`g nufuga`g eheieg ncipug`g F bega`g ncipug`g K

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I`o` omipmscsc reh`sc [ b`g V, sef`a`c fercout <

 

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Bc`ar`i p`g`n

E. VEH@[C G-@VS Veh`sc ieganufugao`g fefer`p` (g) ncipug`g. 

Lco` g 7 6, reh`sc bcsefut reh`sc g-`ry

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Veh`sc g-`ry ieichcoc per`g pegtcga b`h`i f`scs b`t`.

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Ics. @0, @6,…,@g `b`h`n ncipug`g. I`o` reh`sc g-`ry p`b` ncipug`g tersefut `b`h`n <

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@0, @6,…,@g bcsefut bmi`cg, g bcsefut ber`l`t

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Kmgtmn <

F@[C[ B@R@ 

Ouipuh`g t`feh, s`h`n s`tu imbehgy` y`ctu imbeh f`scs b`t` reh`scmg`h. Bcb`s`ro`g p`b` omgsep reh`sc g-`ry.

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T`b` f`scs b`t` reh`scmg`h, tc`p t`feh iegy`t`o`g s`tu reh`sc. [etc`p omhmi p`b` t`feh bcsefut `trcfut. B`er`n `s`h `trcfut `b`h`n ncipug`g teip`t seiu` `gaamt` `trcfut fer`b`.

 

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Rc`p t`feh p`b` f`scs b`t` bcgy`t`o`g sek`r` jcsco b`h`i fegtuo jche, s`tu f`rcs b`t` p`b` t`feh iegy`t`o`g sefu`n rekmrb, b`g setc`p `trcfut iegy`t`o`g sefu`n jcehb.

MTEV@[C T@B@ F@[C[ B@R@ VEH@[CMG@H 

Mper`sc y`ga bch`ouo`g tern`b`p f`scs b`t` bch`ouo`g ieh`huc ‘percgt`n pert`gy``g’ `t`u ‘query query’’ 

 Puery tern`b`p f`scsb`t` reh`scmg`h b`p`t bcgy`t`o`g sek`r` `fstr`o bega`g mper`sc p`b` reh`sc g-`ry

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 Ugtuo ieg`ipcho`g n`sch query, `b` fefer`p` mper`sc y`ga bcaug`o`g <

`) [eheosc Ieichcn f`rcs tertegtu b`rc su`tu t`feh y`ga ieiegunc persy`r`t`g tertegtu Mper`tmr <   f) Trmyeosc Ieichcn omhmi tertegtu b`rc su`tu t`feh Mper`tmr <  k) Lmcg Iegaa`fugao`g bu` fu`n t`feh iegl`bc s`tu, fch` oebu` t`feh ieichcoc `trcfut y`ga s`i` Mper`tmr < 

J. JUGA[C B@G [CJ@R-[CJ@R JUGA[C 0. Jugasc Veh`sc fcger j fcger j b`rc ncipug`g @ oe ncipug`g F, ierup`o`g su`tu jugasc lco` setc`p eheieg bc b`h`i ncipug`g @ bcnufugao`g bega`g tep`t s`tu eheieg bega`g ncipug`g F.

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Lco` j(`)9f, Lco`  j(`)9f, i`o` f f`y`ga`g b`rc `. B`g ` bcsefut pr`-f`y`ga`g b`rc f. b`rc f.

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Ncipug`g y`ga fercsc seiu` gch`c peiet``g j peiet``g  j bcsefut leh`l`n (r`gae (r`gae)) j 

 

6. Jugasc < Veh`sc Onusus 

Oeonusus`g < 0) Rc`p eheieg b`rc bmi`cg j bmi`cg j n`rus bcaug`o`g 6) (`,f) ∌   jj ∡ (`,k) ∌  j  j ↖ f 9 k

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[pescjco`sc jugasc < 0) Ncipug`g p`s`ga`g terurut 6) Jmriuh` pegacsc`g gch`c (`sscagiegt  ( `sscagiegt ) ;) Jugasc b`p`t bcgy`t`o`g bega`g r`gao`c`g o`t`-o`t` 2) Ombe prmar`i ( smurke  smurke kmbe) kmbe)

;. [`tu-oe-s`tu / Cgleotcj  

[cj`t jugasc bchcn`t b`rc f`y`ga`ggy`

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Jugasc j Jugasc  j bco`t`o`g s`tu-oe-s`tu lco` tcb`o `b` 6 eheieg ncipug`g ` y`ga ieichcoc f`y`ga`g s`i`.

 

2. T`b` / [urleotcj 

Jugasc Jug asc  j bcgy`t`o`g surleotcj lco` setc`p eheieg ncipug`g F ierup`o`g f`y`ga`g b`rc 0 eheieg `t`u hefcn eheieg b`rc ncipug`g @.

5. Feromrespmgbeg s`tu-oe-s`tu / Fcleosc 

Jugasc j Jugasc  j bco`t`o`g fcleosc lco` c` `b`h`n jugasc cgleotcj b`g jugasc surleotcj.

:. Jugasc Cgvers 

Lco` j Lco`  j `b`h`n jugasc feromrespmgbeg 0-oe-0 b`rc @ oe F, i`o` oct` b`p`t iegeiuo`g f`hco`g `t`u cgversc b`rc j. b`rc j.

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Bch`if`gao`g bega`g bega`g j   j -0 , lco` j(`) lco` j(`) 9 f. f.

 

A. OMITM[C[C JUGA[C B@G FEFEV@T@ JUGA[C ONU[U[ 0. Omipmscsc Jugasc O`reg` jugasc ierup`o`g fegtuo onusus b`rc reh`sc, oct` lua` b`p`t ieh`ouo`g omipmscsc b`rc 6  fu`n jugasc.

OMITM[C[C JUGA[C RCB@O OMIUR@RCJ 

Omipmscsc bu` jugasc j jugasc j b`g b`g a  a tcb`o omiut`tcj, oeku`hc lco` j lco`  j 9 a 

6. Fefer`p` Jugasc Onusus 0) Jugasc Jhmmr  Ieifuh`to`g fch`ga`g x ∌ V, oe f`w`n. Kmgtmn < _4.5Y 9 4

6) Jugasc Kechcga Ieifuh`to`g fch`ga`g x ∌ V, oe `t`s. Kmgtmn < _4.5Y 9 0

;) Jugasc Imbuhm Ics` Ic s`ho ho`g `g ` `b`h `b`h`n `n seif`r seif`r`ga` `ga`g g fch`ga` fch`ga`g g fuh`t fuh`t b`g i `b`h`n fch`ga`g fuh`t pmsctcj, pmsctcj, jugasc imbuhm `b`h`n jugasc bega`g mper`tmr imb.

 

` imb i ieiferco`g scs` peif`ac`g fch. fuh`t fch` ` bcf`ac bega`g i. Kmgtmn < 65 imb 1 9 2 2) J`otmrc`h

Kmgtmn < 4! 9 0

5) Eospmgegsc`h

Kmgtmn < 2; 9 2.2.2 9 :2

:) Hma`rctico 

Kmgtmn < 2hma :2 9 ;

;. Jugasc Veourscj   j bco`t bco`t`o`g `o`g jugasc reourscj reourscj lco` bejcgcsc bejcgcsc jugascgy` iega`ku p`b` bcrcgy` bcrcgy` segbcrc. segbcrc. Jugasc cgc bcsusug mhen 6 f`ac`g < `) F`scs gch`c `w`h tcb`o iega`ku p`b` bcrcgy` segbcrc  f) Veouregs iegbejcgcsco`g `rauiegt jugasc b`h`i tericgmhmay bcrcgy` segbcrc

 

N. VEH@[C OE[ER@V@@G B@G VEH@[C TEGAUVUR@G T@V[C@H 0. Veh`sc Oeset`r``g Veh`sc V p`b` ncipug`g @ bcsefut b csefut reh`sc set`r` lco` c` reohescj, set`gaoup, b`g iegan`gt`r. Ferb`s`ro`g scj`t y`ga bcichcocgy`, oeset`r``g ctu bcleh`so`g sef`a`c fercout < 0) O`reg` reh`sc ferscj`t set`gaoup, bu` eheieg tersefut set`r` 6) O`reg` reh`sc ferscj`t reohescj, setc`p eheieg set`r` bega`g bcrcgy` segbcrc ;) O`reg` reh`sc ferscj`t iegan`gt`r, ` b`g f set`r`

6. Veh`sc Tegaurut`g T`rsc`h Veh`sc V p`b` ncipug`g @ bcsefut reh`sc pegaurut`g p`rsc`h lco` c` rejheoscj, tmh`o-set`gaoup, b`g iegan`gt`r. Fegb`-fegb` bcuruto`g ferb`s`ro`g scj`t tertegtu, tero`b`ga sep`s`ga fegb` p`b` ncipug`g tcb`o fcs` bcuruto`g.

C. OHM[UV VEH@[C Veh`sc ieichcoc ; scj`t < rejheosc, set`gaoup, b`g iegan`gt`r. Ugtuo ieifu`t reh`sc V ieichcoc scj`t y`ga oct` cgacgo`g, i`o` oct` b`p`t ieg`if`no`g su`tu reh`sc f`ru, ics`h reh`sc [ y`ga eheieggy` `b`h`n eheieg t`if`n`g seicgci`h iugaocg p`b` V, `a`r reh`sc tersefut ieichcoc scj`t y`ga oct` cgacgo`g. Veh`sc [ cgc bcsefut ohmsur scj`t tertegtu b`rc V. @b` ; legcs ohmsur < 0) Ohmsur Vejheoscj 

 

6) Ohmsur [et`gaoup

;) Ohmsur Iegan`gt`r  Iegeiuo`g ohmsur iegan`gt`r sefu`n reh`sc bega`g iegegtuo`g p`s`ga`g scipuh ar`j fer`r`n y`ga ternufuga bega`g sefu`n hcgt`s`g.