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- W2744528174 abstract "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." @default.
- W2744528174 created "2017-08-17" @default.
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- W2744528174 date "2017-08-01" @default.
- W2744528174 modified "2023-09-25" @default.
- W2744528174 title "Dushnik-Miller dimension of contact systems of d-dimensional boxes" @default.
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- W2744528174 doi "https://doi.org/10.1016/j.endm.2017.06.075" @default.
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