کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4647522 1342356 2013 7 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Crossing by lines all edges of a line arrangement
کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات گسسته و ترکیبات
پیش نمایش صفحه اول مقاله
Crossing by lines all edges of a line arrangement
چکیده انگلیسی

Let LL be a family of nn blue lines in the real projective plane. Suppose that RR is a collection of mm red lines, different from the blue lines, and that every edge in the arrangement A(L)A(L) is crossed by a line in RR. We show that m≥n−13.5. Our result is more general, and applies to pseudo-line arrangements A(L)A(L), and even weaker assumptions are required for RR. Our result is motivated by the famous conjecture of Dirac about the existence of a line with many intersection points on it in any arrangement of nn nonconcurrent lines in the plane. We draw a possible relation between the two problems.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Discrete Mathematics - Volume 313, Issue 21, 6 November 2013, Pages 2456–2462
نویسندگان
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