pewarnaan pada graph

7/25/2019 Pewarnaan Pada Graph

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PEWARNAAN PADA GRAPH

KELOMPOK 6:A. HAMLAHINDONGIRWAN ABDULLAH

ST. AISYAH S

1/20/16

PEWARANAAN TITIK PADA GRAPH

Bilanan K!"#$a%i&'a(a G"a'!

Bilanan K!"#$a%i&B)*)"a'a K)la+ G"a'!

Ba%a+ A%a+ BilananK!"#$a%i& G"a'!

Al#"i%$a P),a"naan

Ti%i& 'a(a G"a'!

A'li&a+i P),a"naanTi%i& 'a(a G"a'!

PEWARANAAN SISI PADA GRAPH

In()&+ K!"#$a%i& Pa(a

G"a'!Pengklasifikasian Berdasar

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A'li&a+i P),a"naan Si+iPa(a G"a'!

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2/28

Pewarnaan Titik Pada Graph

Mi+al&an G +)*-a! "a'!. S)*-a!'),a"naan& (a"i G a(ala! '),a"naan

+)$-a %i%i& G ()nan $)n-na&an &,a"na +)()$i&ian !ina (-a %i%i& an*)"!-*-nan lan+-n $)n(a'a%&an,a"na an *)"*)(a. i&a G $),a&ili+)*-a! '),a"naan& $a&a G (i&a%a&an(a'a% (i,a"nai ()nan & ,a"na. S)*-a!

'),a"naan& (a"i "a'! G *ia+ana(i%-n-&&an ()nan $)la*)l %i%i&%i%i& (i G()nan ,a"na 1 2 3 4 &.

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3/28


P),a"naan5 "a'! G

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4/28


Mi+al&an G +)*-a! "a'!. Bilanan

K!"#$a%i& 7!"#$a%i8 n-$*)"9 (a"i "a'!G (ila$*an&an ()nan (i()ni+i&an +)*aai *)"i&-%:

( ) G}padak-pewarnaanada|min{k=G

( )G

1/20/16

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5/28


P),a"naan5 "a'! G $)na(iP),a"naan3 "a'!

1/20/16

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6/28


T)#")$a 1:

1. i&a a(a +)*-a! '),a"naan& 'a(a"a'! G $a&a

2. i&a H +)*-a! "a'! *aian (a"i"a'! G $a&a

3. i&a G1 G2 G34 G&a(ala!

$'#n)n$'#n)n "a'! G$a&a

( ) kG

( ) ( )GH

( ) ( ){ }kiGmaksGi

= 1|

1/20/16

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7/28


i&a "a'! G a(ala! "a'! +#n$a&a S)!ina +)$-a %i%i&G (a'a% (i,a"nai ()nan +a%- %i%i&()nan !ana +a%- ,a"na.S)*ali&na i&a G "a'! $'li%()nan n %i%i& $a&a +)%ia' (-a %i%i&G *)"!-*-nan lan+-n. a(i +)$-a

%i%i& G !a"-+ (i,a"nai ()nan ,a"na*)"*)(a

( ) =GE

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8/28


T)#")$a 2i&a "a'! G a(ala! "a'! $'li%()nan n %i%i& $a&ai&a "a'! G a(ala! "a'! +#n$a&a

T)#")$a 3:Mi+al&an G "a'! %a& +#n. G"a'!G *i'a"%i+i i&a (an !ana i&a

T)#")$a ;i&a 7na(ala! +i&)l ()nan n %i%i&

$a&a :

( ) nG =( ) 1=G

( ) 2=G

( )

=ganjilJika,3

genapJika,2

n

nG

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9/28


T)#")$a 5i&a G +)*-a! "a'! +)()"!ana $a&a

( ) ( ) 1+ GG

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10/28


T)#")$a 6:Mi+al&an G "a'! %)"!-*-n ()nani&a "a'! G %i(a& $'li%

$a&a( ) ( )GG

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( ) 3 G


11/28


1.Al#"i%$a '),a"naanBa"i+an S)()"!ana TheSimple SequentialColouring Algorithm9.

2.Al#"i%$a P),a"naanBa"i+anB)+a"U%a$a

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12/28

Pewarnaan Titik Pada GraphAl#"i%$a '),a"naan Ba"i+an S)()"!anaThe Simple Sequential Colouring

Algorithm9.In'-% : G"a'! G ()nan n %i%i&.S%)' 1 : La*)l %i%i& G ()nan


13/28

Pewarnaan Titik Pada GraphAl#"i%$a P),a"naan Ba"i+anB)+a"U%a$a

In'-% : G"a'! G ()nan n %i%i&S%)' 1 : la*)l %i%i&%i%i& "a'! G

()nan


14/28


7#n%#! Al#"i%$a P),a"naan Ba"i+anB)+a"U%a$a

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15/28


7#n%#! Al#"i%$a P),a"naan Ba"i+anB)+a"U%a$a

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16/28


1. P)na(,alan Uian2. P)na(,alan %"-&

P)nan&-% +a$'a!3. P)n)n%-an >")&-)n+i "a(i#

$#*il);. P)$*aian T-a+5. P)n)$'a%an *a!an*a!an

&i$ia +)8a"a )+i)n.

1/20/161/20/16





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17/28


A'li&a+i P)na(,alan Uian:

Berapapaling sedikit jumlah hariyangdibutuhkan untuk jadwal ujian tersebutsedemikiansehingga semua mahasiswadapat mengikuti ujian mata kuliah yangdiambilnya tanpa bertabrakanwaktunya

dengan jadwal ujian kuliah lain yang jugadiambilnya?1/20/161/20/16





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18/28


Ha+il P),a"naan P)na(,alan Uian:

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A

BE

D

C


19/28

Pewarnaan Sisi Pada Graph

S)*-a! '),a"naan +i+i 'a(a"a'! a(ala! '),a"naan+)$-a +i+i 'a(a "a'! %an'aloop. S-a%- '),a"naan @+i+i&-n%-& "a'! G a(ala! +-a%-

')n-naan +)*aian a%a-+)$-a & ,a"na -n%-&$),a"nai +)$-a +i+i (i G+)!ina +)%ia' 'a+an +i+i

an $)$'-nai %i%i&')"+)&-%-an (i*)"i ,a"na an*)"*)(a. i&a G $)$'-nai'),a"naan @+i+i& $a&a(i&a%a&an +i+i+i+i (i G (i,a"nai()nan & ,a"na.

1/20/16





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20/28


7#n%#! '),a"naan +i+i 'a(a"a'!

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21/28

Pewarnaan Sisi Pada GraphIn()&+ &!"#$a%i& "a'! Ga(ala! Mi+al&an G +)*-a!

"a'!. Bilanan an$)na%a&an $ini$-$*ana&na ,a"na an(i')"l-&an -n%-& $),a"nai

+)$-a +i+i G +)()$i&ian!ina +)%ia' (-a +i+i G an%)"&ai% &) %i%i& an +a$a$)n(a'a%&an ,a"na an*)"*)(a. In()&+ &!"#$a%i&(ia%a&an ()nan C(G).Bia+ana ,a"na,a"na an(i-na&an -n%-& $),a"nai +i+i+i+i +-a%- "a'! (ina%a&an

()nan 1 2 34 &.( ) { }Gpada-sisipewarnaanada|min' kkG =

1/20/16





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22/28


7#n%#!:

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G G


23/28


Teorema 7 (Teorema!i"ing)

i&a G "a'! +)()"!ana $a&aG9 # $ (G) # %G9 1

Teorema &i&a G "a'! *i'a"%i+i (an %a&

+#+n $a&a C (G) '% G9.

1/20/16





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24/28


B)"a+a"&an %)#")$a F !ana a(a (-a

&)$-n&inan nilai (a"i in()&+&!"#$a%i& +-a%- "a'! +)()"!anaai%- +a$a ()nan ()"aa%$a&+i$-$na a%a- +a$a ()nan()"aa% $a&+i$-$ (i%a$*a! 1.

G"a'! G (i+)*-% "a'! &)la+ +a%- i&aC(G) ' %G9 1. Dan "a'!

&)la+ (-a i&a C(G) ' %G9.

Mi+alna +i&)l 'anan )na' a(ala!"a'! &)la+ +a%- +)(an&an +i&)l()nan 'anan anil a(ala! "a'!&)la+ (-a. B)i%- -a "a'! $'li%Kna(ala! "a'! &)la+ +a%- -n%-& n

)na' (an -n%-& n anil Kna(ala!

"a'! &)la+ (-a.1/20/16





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25/28


Teorema :Mi+al&an G "a'! ()nan n %i%i& $+i+i (an ()"aa% $a&+i$-$ i&a $ n/2J $a&a G a(ala! "a'! &)la+(-a.

1/20/16





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Ti%i& 'a(a G"a'!A'li&a+i P),a"naan

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26/28

Pewarnaan Sisi Pada GraphPa(a +i+%)$ a"inan $-ni&a+i an$)li*a%&an +)&-$'-lan +)n%"a (an+)&-$'-lan 8!an)l an $)n!-*-n&an

+)n%"a+)n%"a %)"+)*-%. Un%-&$)n#')"a+i&an +i+%)$ %)"+)*-% +)%ia'8!an)l !a"-+ (i*)"i >")&-)n+i %)"%)n%-.S-'aa %i(a& %)"a(i $a+ala! $a&a8!an)l8!an)l an *)"%)$- (i +-a%-+)n%"a %)"%)n%- !a"-+ (i*)"i >")&-an+i

an *)"*)(a. Mini$-$ *ana&na>")&-)n+i an (i')"l-&an -n%-&$)n#')"a+i&an +i+%)$ $-ni&a+i%)"+)*-%. Dala$ !al ini !i$'-nan +)n%"a$-ni&a+i *)"")+'#n()n+i ()nan!i$'-nan %i%i& 'a(a "a'! (an 8!an)l

an $)n!-*-n&an (-a +)n%"a(i'")+)n%a+i&an ()nan +i+i "a'!.")&-)n+i *)"")+'#n()n+i ()nan,a"na +i+i 'a(a "a'!. M)n)n%-&an$ini$-$ *ana&n >")&-)n+i an(i')"l-&an *)"")+'#n()n+i ()nan

$)n)n%-&an in()&+ &!"#$a%i& 'a(a "a'!1/20/16





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27/28


A'li&a+i '),a"naan +i+i 'a(a "a'!&!-+-+na "a'! *i'a"%i+i a(ala! -n%-&$)nn+%"-&+i *--" +an&a" la%in. T)la!(i&)%a!-i l-a+ *a!,a *--" +an&a" la%in*ana& (i-na&an (ala$ +%a%i+%i&a&!-+-+na (ala$ $)$*-a% "an8anan')"8#*aan an )ni+i *--" +an&a" la%in a(ala!+)*-a! *--" +an&a" la%in #"()" n a(ala!$a%"i&+ *--" +ana&a" n n an )n%"i)n%"ina (ila*)l ()nan *ilanan*ilanan1 2 3 ... n +)()$i&ian !ina %i(a& a(a+)*-a! *ilanan $-n8-l l)*i! (a"i +a%-

*a"i+ (an l)*i! (a"i +a%- l#$.7#n%#! *--" +an&a" la%in 5 5 (a'a%(ili!a% +)*aai *)"i&-% :3 ; 5 1 25 1 2 3 ;2 3 ; 5 1

; 5 1 2 31 2 3 ; 5

1/20/16





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28/28


TERIMA KASIH

1/20/16





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pewarnaan pada graph

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