On the Number of Edges of Fan-Crossing Free Graphs

Otfried Cheong; Sariel Har-Peled; Heuna Kim; Hyo Sil Kim

doi:10.1007/s00453-014-9935-z

On the Number of Edges of Fan-Crossing Free Graphs

Otfried Cheong, Sariel Har-Peled, Heuna Kim, Hyo Sil Kim

Computer Science

Research output: Contribution to journal › Article › peer-review

Abstract

A graph drawn in the plane with n vertices is -fan-crossing free for geqslant if there are no edges,e1,…,ek, such that ldots …,ek have a common endpoint and crosses all We prove a tight bound of on the maximum number of edges of a -fan-crossing free graph, and a tight bound for a straight-edge drawing. For geqslant we prove an upper bound of (k-1)(n-2) edges. We also discuss generalizations to monotone graph properties.

Original language	English (US)
Pages (from-to)	673-695
Number of pages	23
Journal	Algorithmica
Volume	73
Issue number	4
DOIs	https://doi.org/10.1007/s00453-014-9935-z
State	Published - Dec 1 2015

Keywords

Crossing number
Graph drawing
K-planar graphs

ASJC Scopus subject areas

Computer Science(all)
Computer Science Applications
Applied Mathematics

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10.1007/s00453-014-9935-z

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abstract = "A graph drawn in the plane with n vertices is -fan-crossing free for geqslant if there are no edges,e1,…,ek, such that ldots …,ek have a common endpoint and crosses all We prove a tight bound of on the maximum number of edges of a -fan-crossing free graph, and a tight bound for a straight-edge drawing. For geqslant we prove an upper bound of (k-1)(n-2) edges. We also discuss generalizations to monotone graph properties.",

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author = "Otfried Cheong and Sariel Har-Peled and Heuna Kim and Kim, {Hyo Sil}",

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AU - Cheong, Otfried

AU - Har-Peled, Sariel

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AU - Kim, Hyo Sil

PY - 2015/12/1

Y1 - 2015/12/1

N2 - A graph drawn in the plane with n vertices is -fan-crossing free for geqslant if there are no edges,e1,…,ek, such that ldots …,ek have a common endpoint and crosses all We prove a tight bound of on the maximum number of edges of a -fan-crossing free graph, and a tight bound for a straight-edge drawing. For geqslant we prove an upper bound of (k-1)(n-2) edges. We also discuss generalizations to monotone graph properties.

AB - A graph drawn in the plane with n vertices is -fan-crossing free for geqslant if there are no edges,e1,…,ek, such that ldots …,ek have a common endpoint and crosses all We prove a tight bound of on the maximum number of edges of a -fan-crossing free graph, and a tight bound for a straight-edge drawing. For geqslant we prove an upper bound of (k-1)(n-2) edges. We also discuss generalizations to monotone graph properties.

KW - Crossing number

KW - Graph drawing

KW - K-planar graphs

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JF - Algorithmica (New York)

SN - 0178-4617

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ER -

On the Number of Edges of Fan-Crossing Free Graphs

Abstract

Keywords

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