Proper Bounded Edge - Colorings ( Extended Abstract )
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چکیده
For an n-element set X and a proper coloring ∆: [X] −→ {0, 1, . . .} where each color class is a matching with cardinality bounded by u, we show that there exists a totally multicolored subset Y ⊆ X with |Y | ≥ max { c1 · ( n/u ) 1 2k−1 , c2 · ( n/u ) 1 2k−1 · ( ln ( u/ √ n )) 1 2k−1 } This bound is tight up to constant factors for u = ω(n ) for any > 0. Moreover, for fixed k, we give a polynomial time algorithm for finding such a set Y of guaranteed size.
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تاریخ انتشار 2011