کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5777489 | 1632921 | 2017 | 5 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Minkowski complexes and convex threshold dimension
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات گسسته و ترکیبات
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
For a collection of convex bodies P1,â¦,PnâRd containing the origin, a Minkowski complex is given by those subsets whose Minkowski sum does not contain a fixed basepoint. Every simplicial complex can be realized as a Minkowski complex and for convex bodies on the real line, this recovers the class of threshold complexes. The purpose of this note is the study of the convex threshold dimension of a complex, that is, the smallest dimension in which it can be realized as a Minkowski complex. In particular, we show that the convex threshold dimension can be arbitrarily large. This is related to work of Chvátal and Hammer (1977) regarding forbidden subgraphs of threshold graphs. We also show that convexity is crucial this context.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Combinatorial Theory, Series A - Volume 151, October 2017, Pages 202-206
Journal: Journal of Combinatorial Theory, Series A - Volume 151, October 2017, Pages 202-206
نویسندگان
Florian Frick, Raman Sanyal,