Grafy Grafy[02] id 704802 Nieznany

background image







 

 

! #" $&%'$)(+*-,.0/1*32547698;:=<

>?6A@B8DC

>E,FHGIJG <K,L*M@NFBO1IP<RQSIB*7THUAV12WX>QY4[Z\4]QX,\G=^5_MZ`THI

4-2NabZ:Ob,Tc8<d,\Ce8gfE*A,h.iIjC

k'l[mon'pqsr

t

436]O1QSI7_uIvG25>1W&,\G=O1QSIw_uIBGIjOx476y,O1Gz,\*MG2B<d8

n

{

<RQ|IB*3THUAV12 WX>}2B<d8xfE*A,h.~/I\WXO?8;: >?6-@

{

*3Ijf}2`<€Q|IB*3THUAV12 WX>E,CQ‚4[Zsƒ|QSUjTBa?8

1, 2, . . . , n

„

25TBOb,\UjTBC…8†fE2‡438 CLaˆ2Eƒ|IjC

K

n

r

‰

,\FHG 8

n

{

<RQ|IB*3THUAV12 WX>}2B<d8ŠfE*-,./I\WXO?8‹Q|TH2NC25*7Œ'UjTBO?8`_uIj436KT

K

n

r



‹ #" $&% Ž

! #" $" $(+*-,.

H

⊆ G

_uIj436+‘\’”“‘E•`<

fE*-,Œ'I

G

<6-IBG 8†Qˆ6–8Dƒ|>E2s<6AIBG 8;: fEG 8—_uIj436

fE*A,h.iIjC

/I\WXO?8 Cr

∗ ω(G) =

Cx,H˜

{|V (H)| : H

_uIj476€>ƒSQ™>EZe<

G

}

6-2šƒ|QSUjTBab,›‘’”“‘5œNwžšfE*A,h.#^

G

r

Ÿ

ƒ,L>5,\FHGIjfE2‡fE*A,h.#^

ω

(G) ≥ 1

Q

ω

(G) ≤ ∆(G) + 1

r

 

Q|UjTBab,L>ƒ|Q|>E2H<d,+_7Ij476€/b,\*A,CIy6-*3IjC

6-*3^1G=O?8 C

2Na1ƒSQ|UjTHIjO1Q|2H<2=r



‹ #" $"'Ž

! #" $S¡‚$K(+*-,.w/1*M2N436–8;:‚<

>;6-@5*u8 C

F,G=O1IsG <d,›<€Q|IB*3THUAV12 WX>Q¢O1Q|Is4£Z4-Q,G=^5_MZxTHI

4-2NabZ:Ob,Tc8<d,\Ce8gfE*A,h.iIjC

kˆ¤?¥j¦&pqsr

t

436]O1QSI7_uIvG25>1W&,\G=O1QSIw_7IBGIjO§476y,O1Gz,*3G2H<8

n

{

<RQSIB*7THUAV12WX>E2H<8†f}*-,.¨/^43698;:>?6-@

{

*3Ijf}2`<€Q|IB*3THUAV12 WX>E,CQ‚4[Zsƒ|QSUjTBa?8

1, 2, . . . , n

„

25TBOb,\UjTBC…8†fE2‡438 CLaˆ2Eƒ|IjC

N

n

r

‰

,\FHG 8

n

{

<RQ|IB*3THUAV12 WX>}2B<d8©fE*-,. /I\WXO?8+Q|TH2NC25*7Œ'UjTBO?8_uIj436YT

N

n

„

TBa1Q|@E*> *-,c<ªBG=THQ

G2H<2Eƒ™O1IjfE2šf}*-,h.i^/^436-IjfE2J_uIj436KTBa1QS25*3IjC

/^436–8 Cr

∗ K

1

= N

1

2E*-,T

N

n

⊆ K

n

GƒX,—>E,FHGIjf}2

n

r

«D¬­¬S¬

background image

! #" $~$ba1QS@5*

U

⊆ V

_uIj436PTBa1Q|2E*3IjC

n'“

l

ž5’­lcn1pq

<

f}*-,Œ'I

G

= (V, E, ψ)

<6AIBG 8gQ6–8Dƒ|>E2<6AIBG 8;:=f}G=^

U

= ∅

ƒ|^a

G

[U ]

_uIj436Kf}*-,h.&IjC

/^43698 CŠr

∗ α(G) =

Cx,H˜

{|U | : U

_7Ij476€TBa1Q|2E*3IjC

O1Q|IjT,\ƒSIjFBO?8 C

<

G

}

6A2§ƒ|QSUjTBab,Šn1“

l

ž

’­lcnˆœ j“<RQSIB*7THUAV12WX>E2H<I7_dfE*A,h.#^

G

r

∗ 1 ≤ α(G) ≤ |V | − δ(G)

25*-,\T

α

(G) + ω(G) ≤ |V | + 1

r

 

Q|UjTBab,LO1Q|IjT,ƒ|IjFBO12 -UBQ_uIj436K/b,\*A,CIy6-*MIjC

6A*7^1G=O?8DC

25a1ƒ|Q|UjTHIjO1QS2B<2=r



‹ #" $S¡bŽ

! #" $ $(+*-,.

G

= (V, E, ψ)

_uIj436df}*-,h.&IjC

r

Al5¤D’|žyn1pq

AlE¤ ’|ž£n1pq

¥j¦

œAk

n1“ož

r



<d6-IBG 8

QK698Dƒ|>E2

<6-IBG 8;:RfEG 8

deg

(v) = r

GƒX,

>E,FHGIjf}2

<RQSIB*7THUAV12WX>5,

v

∈ V

r

‰

,\FHG 8†fE*A,h./^43698`_uIj436Kf}*-,h.&IjC

0

{

*3Ijf5^1ƒX,\*3O?8 Cr

‰

,\FHG 8

n

{

<RQ|IB*3THUAV12 WX>}2B<d8ŠfE*-,./I\WXO?8L_7Ij476RfE*-,.iIjC

(n − 1)

{

*3IjfE^1ƒ,\*3O?8 Cr

(J*-,h.

8

3

{

*MIjf5^1ƒX,\*7O1I

6-2

f}*-,h.

8

‘\¤j“ cn l

„

Q|U[V

/2 G=fE*A,h.X8

&2

<€Q|IB*7THU[V12 WX>E,\UAV

436-2N/O1QX,

0, 1, 2

Ī^a

3



6-2‡fE*A,h.X8xkœ\‘\¤c“ cn lcr



‹ #" $ Ž

! #" $ ‚$"!;6y,O1Gz,*3G2H<8

fE*-,.+/1*M2N436–8;:

>?6-@E*3Ijf}2

<€Q|IB*3THUAV12 WX>E,CQK4[Z

<K4]Tc8 436]>QSI

k

{

IBƒSIjCšIjO;6-2H<I…UBQZEf}Q¨a1Q™Ob,\*3O1IeQ <

>?6-@E*

8 C

>*A,y<ªBG=THQ|I‡W&Z\UjTZL698Dƒ™>}2š6-I©4M/2 -*3@G

UBQZ}fE@H<e:>;6-@5*MIx*M@NFBO1QZ

4-Q|ª§G25>1W&,\G=O1QSI…_uIBG=O?8DC

IBƒ|IjCIjO?6AIjCŠ:25TBOb,\UjT,C…8

Q

k

Q

Ob,Tc8<d,\Ce8

k



‘5œ¥j¦#‘5•#9¥y¤

k'l$A‘Eœh¥j¦#‘E•



r

!^/IB*7>}2N436]>E,

Q

k

C§,

2

k

<€Q|IB*3THUAV12 WX>}@B<

Q

k

2

k

−1

>*A,y<ªBG=THQor

!^/IB*7>}2N436]>E,

Q

k

_uIj476€fE*A,h.iIjC

k

{

*MIjf5^1ƒX,\*7O;8 CŠr

∗ Q

1

= K

2

r

¬&%

background image

! #" $ $x(J*-,h.

G

= (V, E, ψ)

_7Ij476

f}*-,.iIjC

N

¤

c“

lc’”n1pq

<6-IBG 8

QJ6–8Dƒ|>E2

<6AIBG 8;:©fEG 8

Q|476-O1Q|I7_MZ

*325TW&Z\UjTBO1I

TBa1QS25*

8

O1Q|IjT,\ƒSIjFBO1I

V

1

, V

2

⊆ V

6£,> Q|IE:©FHI

V

1

∪ V

2

= V

r



2 G=THQ|Ob,

{V

1

, V

2

}

6-2

kœ

c“ož\m

N

¤

c“

ly’”n1psfE*A,h.#^

G

:D,JTBa1QS25*

8

V

1

, V

2

6-2

kž



¦&p

hl

N

¤

c“

ly’”nˆœ j“fE*-,.#^

G

r



2G=fE*-,.1fE*A,h.#^sG <R^1G=THQ|IBĪO1Ijf}2_uIj436fE*A,h.iIjC

G <K^1G=THQSIBĪO?8 C

„

fE*A,h.X8LG <K^1G=THQ|IBƒ|O1I

O1Q|IJC2Nf ZL/254]QX,\Gz,©/ˆªy6Aƒ|Q

r



‹ #" $'Ž

!/2 -*3@ G‹2NC@H<RQ|25O?8DUAV

G2…6AI7_/2E*

8§fE*A,h.i@H<e:=fE*-,.

,CQ G <R^1G=THQ|IBƒ™O;8 CšQ

4£Z—Cr

Q™OYr<K4]Tc8 436]>QSI

4]^/ˆIB*3>E25476->Qo:'f}*-,h.

8‹/^436-I

Q

1

{

*3Ijf5^1ƒX,\*3O1IEr

! #" $ ‚$!(+*A,h.~/1*32547698

G

= (V, E, ψ)

_7Ij476wk'l[mon'pq



]ž Hlyq

N

¤

c“

ly’”n1pq

<6

{

IBG 8Q 6–8=ƒ™>E2

<6AIBG 8;:?f}G 8sQ|476-O1Q|I7_uI6y,>Q'/ˆ2G=THQ,}WˆG <K^1G=THQSIBƒ™O?8

{V

1

, V

2

}

:EFHI>E,\FHG 8

<RQSIB*7THUAV12W

Ij>

u

∈ V

1

4£Z4-Q,G=^5_uI+<

G

T

>5,\FHG 8 C

<€Q|IB*3THUAV12 WX>QSIjC

v

∈ V

2

r

t

436]O1Q|I7_7I

G2N>1W&,G=O1Q|I_uIBGIjO

436£,\O1Gz,\*MG2B<d8J/I\WXO?8Pf}*-,.=G <R^1G=THQ|IBƒ™O;8;:Gƒ,

>?6-@E*3IjfE2

V

1

= {1, 2, . . . , r}

Q

V

2

= {r +1, . . . , r +s}

„

2NTBOb,UjT,C…8—f}2+478 CLa25ƒSIjC

K

r,s

r

‰

,FHG 8

/ˆI\WXO;8

f}*-,h.G <R^1G=THQ|IBƒ™O;8;:¨Gƒ,§>?6A@5*MIjfE2

|V

1

| = r

2E*-,\T

|V

2

| = s

_uIj436

Q™TH25Cš2E*uŒ'UjTBO?8gT

K

r,s

r

∗ K

1

,1

= K

2

25*A,T

K

2

,2

= Q

2

r



‹ #" $ bŽ

! #" $ ‚$

(J*-,h.

G

= (V, E, ψ)

_7Ij476

f}*-,h.&IjC

k





c“

ly’”n1pq

<6AIBG 8

Q‡698Dƒ|>E2

<6AIBG 8;:Kf}G 8

Q™436]O1Q|I7_]Z

*M2NTW&Z\UjTBO1I

TBa1QS25*

8

O1Q|IjT,ƒ|IjFBO1I

V

1

, . . . , V

k

⊆ V

6£,> Q|IE:

FHI

V

1

∪ . . . ∪ V

k

= V

r

(+*A,h.X8

1

{

G=THQ|IBƒ|O1IP6-2‡fE*-,.X8

/^476AIEr



2 G=f}*-,.

f}*-,.#^

k

{

G=THQ|IBƒ|O1IjfE2s_uIj436©fE*-,.iIjC

k

{

G=THQ|IBƒ|O?8 C

„

fE*A,h.X8

k

{

G=THQ|IBƒ|O1IsO1Q|I

C2Nf;ZL/2N4-Q,\Gz, ©/ªy6-ƒSQor

‰

,\FHG 8

n

{

<RQ|IB*3THUAV12 WX>}2B<d8©fE*-,. aIjT)/ªy6-ƒ|Qj_uIj436¨f}*-,.iIjC

k

{

G=THQ|IBƒ|O?8 C

Gƒ,/ˆIy<RO1IjfE2

k

≤ n

„

>5,\FHG 8†fE*A,h.

k

{

G=THQ|IBƒ|O?8`_7Ij476€fE*A,h.iIjC

l

{

G=THQ|IBƒ|O?8 C

Gƒ,`>5,\FHGIjfE2

l

≥ k

r

%

background image

! #" $&%‚$†(+*-,.s/1*32547698

G

= (V, E, ψ)

_uIj436

k'l[mon1pq



]ž Hl£q

k





c“

lc’

n'pq

<6AIBG 8

Q6–8=ƒ™>E2g<6-IBG 8;:~fEG 8

Q|476-O1Q|I7_MZgO1Q|Ij/^436-IšQ

*32NTW&ZUjTBO1IšTBa1Q|25*u8

O1Q|IjT,ƒ|IjFBO1I

V

1

, . . . , V

k

⊆ V

6£,> Q|IE:FHI

V

1

∪. . .∪V

k

= V

QEGƒX,

>E,FHGIjf}2

i

= 1, . . . , k

:

>E,FHG 8

<RQSIB*7THUAV12W

Ij>

u

∈ V

i

4£Z4-Q,G=^5_uI+<

G

T

>E,\FHG 8 C

<€Q|IB*7THU[V12 WX>QSIjC

v

∈ V \ V

i

r

t

476-O1Q|I7_uIJG25>1W&,\G=O1QSI_uIBGIjO†436£,\O1Gz,\*MG2B<d8g/I\WXO?8xf}*-,h.

k

{

G=THQ|IBƒ|O?8;:DGƒX,—>?6A@5*3Ijf}2

V

i

= {s

i

+ 1, s

i

+ 2, . . . , s

i+1

}

: f}G=THQ|I

s

1

= 0

Q

s

i+1

= s

i

+ r

i

„

25TBOb,\UjT,\Ce8›fE2

438 CLaˆ2Eƒ|IjC

K

r

1

,r

2

,...,r

k

r

‰

,FHG 8

/I\WXO?8

fE*A,h.

k

{

G=THQ|IBƒ™O?8;:GƒX,

>?6-@E*3Ijf}2

|V

i

| = r

i

:

i

= 1, . . . , k

: _7Ij476

Q™TH25Cš2E*uŒ'UjTBO?8gT

K

r

1

,...,r

k

r

! #" $&%'%'$+(+*A,h.

G

= (V, E, ψ)

_uIj436‹n1“

lA¥–k

£n1p

<d6-IBG 8

Q¢698Dƒ|>E2

<6AIBG 8;:)f}G 8

Q™436]O1QSI7_MZ

O1Q|Ij/^436-I€Q'*M2NTW&ZUjTBO1IR/ˆ2G=TBa1Q|25*u8

V

1

, V

2

⊆ V

6£,\>Q|IE:FHI

V

= V

1

∪ V

2

Q

>E,FHGz,LT

>*-,c<ªBG=THQYf}*-,h.i^

G

W&Z\UjTc8x<€Q|IB*3THUAV12 WX>QYOb,ƒ|IjFZ\UBIe*3@H<KO12 UjTHI

]O1Q|I©G2

V

1

ƒ™^aŠ*M@B<RO12 UjTHI

]O1Q|IeG2

V

2

r



‹ #" $'Ž

!/ˆ2

]*M@ G

2NCx,y<€Q,\O?8DUAV

G2g6-I7_+/25*u8

fE*A,h.i@H<e:f}*-,.

,CQ¢4]/@\_uO?8 CQ

4[Z

Cr

Q™OYr)f}*-,.X8‹/I\WXO1IE:D4]^/IB*7>}2N436]>Q¨Q /I\WXO1IJf}*-,h.

8

k

{

G=THQSIBĪO1IE:

k

≥ 2

r



‹ #" $ bŽ

! #" $&% " $D(+*A,h. /1*M2N436–8

G

= (V, E, ψ)

aªBGzZ\Uy8+*M@B<RO12 UjTHI

MO1QSI

fE*A,h.iIjC

4]/@\_uO?8 C

Q

2

{

*3Ijf5^1ƒX,\*3O?8 C

6-2

cp‘’”r



I

-ƒ|Q

n

≥ 3

:H6A2KQ|476-O1Q|I7_uIG2N>1W&,G=O1Q|I¨_uIBGIjO

436£,O1Gz,*3G2H<8…Uy8 > ƒo:>;6-@5*MIjfE2d<€Q|IB*7T

{

UAV12WX>5,\CšQ

4[Z

ƒ|QSUjTBa?8

1, 2, . . . , n

:

,

>*-,c<ªBG=THQX,CQ

TBa1Q|25*u8

{1, 2}, . . . ,

{n − 1, n}, {n, 1}

„

2NTBOb,UjT,C…8†f}2438 CLa25ƒ|IjC

C

n

r

‰

,\FHG 8

n

{

<€Q|IB*7THU[V12 WX>E2H<8‡Uy8D>ƒQ™TH25Cš2E*uŒ'UjTBO?8v_uIj436

T

C

n

„

>E,FHG 8sUy8 >ƒD/2N4-Q,\Gz,

/1*7Tc8DOb,

_uC‡O1QSI7_

3

<€Q|IB*7THU[V12 WX>Q

r



8 > ƒ¢/2N4-Q,Gz,

_]Z\Uy8

/b,*7Tc8 436£Z

ƒ|Q|UjTBaª<RQSIB*7THUAV12WX>E@H<

6A2Uy8 > ƒ0kžcph¥j¦&p

„

Uy8 >ƒ

/2N4-Q,Gz,

_]Z\Uy8

O1Q|Ij/b,\*3Tc8 436£Zƒ|QSUjTBaˆªP<€Q|IB*3THUAV12 WX>}@B<

6A2‡Uy8 > ƒn1“

l–kžcph¥j¦&pNr

∗ C

3

= K

3

Q

C

4

= K

2

,2

r

%=¬

background image



‹ #" $ bŽ

! #" $&% ¡‚$+(+*A,h.R/1*32N43698

aIjT§Uy8 > ƒ|Q



,Uy8 >ƒ|QSUjTBO?8



6A2

’™ž¥

„

ƒX,4`aªBGzZ\Uy8

fE*A,h.iIjC

4]/ˆ@_

O;8 C

6A2#

l£wœ5r

Ÿ

*7THIy<2436-25/O1Q,

0, 1

Ī^a

2

6-2

-UBQ|IjFB>E,r

t

476-O1Q|I7_uILG25>1W&,\G=O1QSI

_uIBG=Ob,‡436£,O1Gz,*3G2H<d,

-UBQ|IjFB>E,:>?6A@5*3I7_K<RQ|IB*3THUAV12 WX>E,\CšQ04[Z

ƒ|QSUjTBa?8

1, 2, . . . , n

:?,€>*-,c<ªBG=THQX,CQ=TBa1Q|2E*

8

{1, 2}, . . . , {n−1, n}

„

2NTBOb,\UjT,\C…8

fE2‡438 CLaˆ2Eƒ|IjC

P

n

r

‰

,\FHGz,

n

{

<RQSIB*7THUAV12WX>E2H<d,

-UBQ|IjFB>E,sQ™TH2NC25*7Œ'UjTBOb,€_uIj436€T

P

n

r

∗ P

1

= K

1

:

P

2

= K

2

Q

P

3

= K

2

,1

r



‹ #" $&%ˆŽ

! #" $&%

~$

!/ˆ@_

O;8

/2 G=fE*A,h.f}*-,.#^

G

_uIj436_uIjf}2¥[‘hm–ž

?œNw•x4]/@\_uO12 -UBQ~<d6-IBG 8

Q

698Dƒ™>}2š<6AIBG 8;:'fEG 8Š>E,FHG 8_uIjfE2Ob,G=fE*-,.<+W&, -UBQ

<d8aªBGzZ\Uy8

/ˆ2G=fE*-,.iIjC

G

_7Ij476

fE*A,h.iIjC

O1QSIj4M/@_

O?8 Cr



‹ #" $&%'%DŽ

%=¬­¬

background image

! #" $&%

 $dQSIBUAV

G

aªBG=THQ|I

f}*-,h.&IjCŠr

b¤ qš•

f}*-,.i@B<

G

1

, G

2

⊆ G

Ob,\Tc8

{

<K,C…86-IjO§4]/2 -*3@ G†/2 G=fE*A,h.i@H<

fE*A,h.#^

G

: >?6-@IjfE2LTBa1Q|2E*3IjC

<€Q|IB*3THUAV12 WX>}@B<

_7Ij476

V

(G

1

) ∪ V (G

2

)

Q‚>?6-@E*3Ijf}2TBa1QS25*3IjC

>*A,y<ªBG=THQ=_uIj476

E

(G

1

) ∪ E(G

2

)

r

!^CªLfE*A,h.i@H<

G

1

Q

G

2

25TBOb,\UjT,\Ce8

478DC—a2Eƒ|IjC

G

1

∪ G

2

„

_uI7_K<K,\*u6-2

+_uIj476

O1Q|IjT,ƒ|IjFBOb,s2 G†<8Daˆ2E*7^Šf}*-,.#^

G

r



W&,\4MO12

]UBQJ4]^C…8

f}*-,h.&@B<

4£Z

/2 G2NaO1I

G2

<JW&,4]O12 -UBQ

4M^C…8

TBa1Q|2E*3@H<

„

<

4]THUjTHIjfE@5ƒ|O12 -UBQ_uIj476€2NOb,›W&Z\UjTBOb,`Q/1*3THIjCšQSIjOOb,r

(+*A,h.z_uIj436K4]/@\_uO?8§<6AIBG 8‹Qb698Dƒ™>}2`<d6-IBG 8;:=fEG 8†O1QSIPC2NFBOb,—fE2s/1*3THIBG=476y,y<€Q

+<

/2N436£,UBQ4]^C…8†fE*A,h.i@H<

2‡*M2NTW&Z\UjTBO;8DUAVŠTBa1QS25*-,UAVg<€Q|IB*7THU[V12 WX>E@H<er



‹ #" $&% "zŽ

! #" $&%

‚$Y(+*A,h./1*M2N436–8

G

= (V, E, ψ)

_7Ij476K‘Eœ\m

lyq

<d6-IBG 8šQ6–8=ƒ™>E2©<6AIBG 8;:?f}G 8

/2N4-Q,Gz,d<€Q|IB*7THU[V12 W

Ij>

v

6£,\>Qo:}FHI

V

\{v} = N (v)

25*A,Tf}*-,.

G

−v

_uIj436¢Uy8 >ƒ|IjC



IjFHIBƒSQ

n

≥ 4

:;6-2LQ™436]O1QSI7_uIJG2N>1W&,G=O1Q|I

_uIBG=O12—476y,O1Gz,*3G2H<IJ>}2 W

2=:=Gƒ,e>?6A@5*3Ijf}2

V

= {1, 2, . . . , n}

:

v

= n

Q

G

− v = C

n

−1

„

25TBOb,\UjT,C…8L_7IJ478 CLa25ƒSIjC

W

n

r

‰

,\FHGI

n

{

<€Q|IB*7THU[V12 WX>E2H<Ie>}2 W

2Q™TH25Cš2E*uŒ'UjTBO1I_uIj436RT

W

n

r

∗ W

4

= K

4

r



‹ #" $&% ¡ˆŽ

%D¬­¬S¬

background image

! #" $&%

$€(J*-,h.&IjC

‘ ]žN

c“oœN

pq

O1QSIj/^476AIjfE2fE*-,.#^

G

= (V, E, ψ)

Ob,\Tc8

{

<K,C…8§476y,O1Gz,\*MG2B<d8†fE*A,h.!/1*M2N436–8

L

(G)

:>?6-@E*3IjfE2sTBa1Q|25*MIjC

<RQSIB*7THUAV12WX>E@H<

_uIj436

E

:‚,‡G <d,s<€Q|IB*3THUAV12 WX>Q

e

1

Q

e

2

4[Z\4]QX,\G=^5_MZTHIe4-2NabZs<d6-IBG 8QY698Dƒ™>}2<d6-IBG 8;:bf}G 8

>*A,y<ªBG=THQ|I

e

1

, e

2

4£Z—4£Z4-Q|IBG=O1QSI+<

f}*-,Œ'I

G

r



‹ #" $&%

! #" $&%

‚$—œAkzlAm

n1“

lyn1“

l£q

fE*A,h.#^

/1*M2N436-IjfE2

G

= (V, E, ψ)

Ob,Tc8<d,\Ce8

436£,\O

{

Gz,\*u6-2H<8

fE*A,h.R/1*32N43698

G

:0>?6A@5*3Ijf}2

TBa1Q|2E*3IjC

<RQ|IB*3THUAV12 WX>}@B<

_7Ij476`TBa1Q|@E*

V

Q

<

>?6A@5*

8DC

G <d,<RQSIB*7THUAV12WX>Q

4£Z4-Q,G=^5_MZxTHI`4-2NabZ<6AIBG 8

Q0698Dƒ™>}2†<6-IBG 8;:YfEG 8

O1Q|I

4£Z4-Q,\G=^5_]Z—<

fE*A,hŒ'I

G

r

(J*-,h.7:>?6-@H8…_uIj476Q|TH2NC25*uŒ'UjTBO;8THIvTc<2EQ™C

G2N/I\WXO1QSIjO1Q|IjC

6-2—fE*A,h.

¥HžNqšœ?œ[k'l[m

n1“ož

B•

jpNr

Ÿ

25/I\WXO1Q|IjO1Q|I

fE*A,h.#^

*MIjf5^1ƒ,*7O1Ijf}2

_uIj436

fE*A,h.iIjC

*3Ijf5^1ƒX,\*3O?8 C

„

G2N/I\WXO1Q|IjO1QSI

fE*A,h.#^

/^436-Ijf}2x_uIj436‡fE*A,h.iIjC

/I\WXO?8 C:,

G25/I\WXO1Q|IjO1Q|I‹f}*-,h.i^

/ˆI\WXO1Ijf}2

fE*A,h.iIjC

/^436–8 Cr

Ÿ

ƒ,L>5,\FHGIjfE2‡fE*A,h.#^Š/1*M2N436-Ijf}2=:

ω

(G) = α(G)

r

Ÿ

ƒ,L>5,\FHGIjfE2‡fE*A,h.#^Š/1*M2N436-Ijf}2=:

δ

(G) + ∆(G) = δ(G) + ∆(G) = |V | − 1

r



‹ #" $&%

zŽ

%D¬

«


Wyszukiwarka

Podobne podstrony:
Grafy Zadania id 704808 Nieznany
HUR2006 02 id 207255 Nieznany
26429 02 id 31504 Nieznany (2)
CwiczenieArcGIS 02 id 125937 Nieznany
awans 02 id 74352 Nieznany (2)
Zestaw 02 id 587899 Nieznany
cwiczenie 02 id 125037 Nieznany
Perswador 02 id 354972 Nieznany
Axis se 02 id 74597 Nieznany
chorg01 02 id 114495 Nieznany
Graphic 02 id 195493 Nieznany
Krym 02 id 251310 Nieznany
mt2009 02 id 310143 Nieznany
MD cw 02 id 290123 Nieznany
dzieje poprz 20 02 1 id 147967 Nieznany
A gdziez ow Szwed v 02 id 49220 Nieznany
Mechanika gruntow W 02 id 29095 Nieznany
projekt 06 przyklad 02 id 39794 Nieznany

więcej podobnych podstron