کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5777109 | 1632570 | 2017 | 7 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Dushnik-Miller dimension of contact systems of d-dimensional boxes
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات گسسته و ترکیبات
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
Planar graphs are the graphs with Dushnik-Miller dimension at most three (W. Schnyder, Planar graphs and poset dimension, Order 5, 323-343, 1989). Consider the intersection graph of interior disjoint axis-parallel rectangles in the plane. It is known that if at most three rectangles intersect on a point, then this intersection graph is planar, that is it has Dushnik-Miller dimension at most three. This paper aims at generalizing this from the plane to Rd by considering tilings of Rd with axis parallel boxes, where at most d+1 boxes intersect on a point. Such tilings induce simplicial complexes and we will show that those simplicial complexes have Dushnik-Miller dimension at most d+1.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Electronic Notes in Discrete Mathematics - Volume 61, August 2017, Pages 467-473
Journal: Electronic Notes in Discrete Mathematics - Volume 61, August 2017, Pages 467-473
نویسندگان
Mathew C. Francis, Daniel Gonçalves,