A central approach to bound the number of crossings in a generalized configuration
نویسندگان
چکیده
A generalized configuration is a set of n points and (n 2 ) pseudolines such that each pseudoline passes through exactly two points, two pseudolines intersect exactly once, and no three pseudolines are concurrent. Following the approach of allowable sequences we prove a recursive inequality for the number of (≤ k)-sets for generalized configurations. As a consequence we improve the previously best known lower bound on the pseudolinear and rectilinear crossing numbers from 0.37968 ( n 4 ) + Θ ( n 3 ) to 0.379972 ( n 4 ) +Θ ( n 3 ) .
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ورودعنوان ژورنال:
- Electronic Notes in Discrete Mathematics
دوره 30 شماره
صفحات -
تاریخ انتشار 2008