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The maximal sizes of faces and vertices in an arrangement

Authors
Journal
Discrete Mathematics
0012-365X
Publisher
Elsevier
Publication Date
Volume
28
Issue
3
Identifiers
DOI: 10.1016/0012-365x(79)90142-0

Abstract

Abstract Let A be an arragement of n lines in the plane. Suppose that F 1,…, F r are faces of A and that V,…, V s are vertices of A. Suppose also that each F i is a (V j ) of the lines of A intersect at V j . Then we show that ∑ i=1 r t(F i + ∑ j=1 s t(V j)⩾n+4 r 2 + s 2 + 2rs .

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