р⎭Ӛ䙐ཝᆜ䈋ভ
˄kyky 㠣 kykR ᆖᒤ ㅜ k ᆖᵏᵏᵛ㘳䈅˅
⨝㓗˖
ᆖ˖ ဃ˖
䈮〻〠˖ 㓴ᮠᆖ ᡀ㔙˖
ж URy ࠶Vǃ≲ᆇㅖѢ 123456 ᧂࡇⲴњᮠˈ֯ᗇަѝ⋑ᴹࠪ⧠ᒿࡇ 12ǃ23ǃ34ǃ45ǃ56DŽ
ӂ URy ࠶Vǃањⴂᆀ䟼ᴹ 30 њ㓒⨳ǃ40 њ㬍⨳઼ 50 њⲭ⨳ˈ仌㢢Ⲵ⨳ᱟᰐ⌅࠶
ⲴDŽӾⴂᆀѝࠪ 70 њ⨳ˈᴹཊቁнⲴ⌅˛
R
ᡇᢵ䈰θᡇሼћṲ
䚫ᆾ㘹䈋㓠ᗁȾ
ᢵ䈰Ӱφ
仈 а Ҽ й ഋ ӄ ޝ г ޛ ҍ
ᗇ࠶
ᢩ䰵Ӫ
U⍱≤䰵V
п URy ࠶V ǃ
URV ≲䳶 A
1
,A
2
, ···A
k
䘹Ⲵᯩ⌅ᮠˈ֯ᗇ ∅ ⊆ A
1
⊆···⊆A
k
⊆ [n]DŽ
UkV ≲ [n] Ⲵᆀ䳶 A
1
,A
2
, ···A
k
䘹Ⲵᯩ⌅ᮠˈ֯ᗇ A
1
∩···∩A
k
= ∅DŽ
URy ࠶Vǃ䇮 |X| = n ф F ᱟ X
(k)
Ⲵᆀ䳶DŽᇊѹ ∇F =
T ∈ X
(k+1)
|∃S ∈F ֯ᗇ
S T }DŽ䇱᰾ྲ k ≤
n−1
2
ˈࡉᴹ |∇F| ≥ |F|DŽަѝˈX
(i)
㺘⽪ X Ⲵᡰᴹ i ݳᆀ䳶ᡰ
㓴ᡀⲴ䳶㌫DŽ
k
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