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The Crossing Lemma for Multigraphs Toth, Geza
Description
The crossing number $cr(G)$ of a graph $G$ is the minimum number of crossings over all possible drawings of $G$ on the plane. According to the Crossing Lemma, for any simple graph $G$ with $n$ vertices and $e\ge 4n$ edges, $cr(G)\ge {1\over 64}{e^3\over n^2}$. Clearly, this result does not hold for multigraphs (graphs with parallel edges or loops). We find natural conditions that imply the analogue of the Crossing Lemma for multigraphs.
Item Metadata
| Title |
The Crossing Lemma for Multigraphs
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| Creator | |
| Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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| Date Issued |
2018-02-05T14:05
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| Description |
The crossing number $cr(G)$ of a graph $G$ is the minimum number of crossings
over all possible drawings of $G$ on the plane.
According to the Crossing Lemma, for any simple graph $G$
with $n$ vertices and $e\ge 4n$ edges, $cr(G)\ge {1\over 64}{e^3\over n^2}$.
Clearly, this result does not hold for multigraphs (graphs with parallel edges
or loops). We find natural conditions that imply the analogue of the
Crossing Lemma for multigraphs.
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| Extent |
35 minutes
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| Subject | |
| Type | |
| File Format |
video/mp4
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| Language |
eng
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| Notes |
Author affiliation: Renyi Institute of Mathematics
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| Series | |
| Date Available |
2018-08-05
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| Provider |
Vancouver : University of British Columbia Library
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| Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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| DOI |
10.14288/1.0369711
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| URI | |
| Affiliation | |
| Peer Review Status |
Unreviewed
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| Scholarly Level |
Faculty
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| Rights URI | |
| Aggregated Source Repository |
DSpace
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Rights
Attribution-NonCommercial-NoDerivatives 4.0 International