The Probabilistic Method by Noga Alon & Joel H. Spencer

Author:Noga Alon & Joel H. Spencer [Alon, Noga & Spencer, Joel H.]
Language: eng
Format: epub
Published: 2011-02-19T05:00:00+00:00

Ó´Ò

µ

Ù¾Î

Ù

Ú

and by summing over all vertices

we conclude that

satisfies property

.

Ú

È

6.

.

È

µ

È

´×µ

ÓÖ

Ð Ð

×

½

½

Suppose

satisfies

. For any two distinct vertices

and

of

let

´Î

µ

È

Ù

Ú

be

if

and

otherwise. Also, define

´Ù

Ú µ

½

ÙÚ

¾

¼

×´Ù

Ú µ

Û

¾

Î

´Ù

Û µ

. Since

is

½

-regular,

´Ú

Û µ

´

·

Ó´½µµÒ

×´Ù

Ú µ

¾

Æ

´Ùµ

Æ

´Ú µ

·

Ò

¾

¾

. Therefore, the fact that

satisfies

implies that

¾

Æ

´Ùµ

Æ

´Ú µ

·

Ó´Òµ

È

Ò

¿

(9.2)

×´Ù

Ú µ

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