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2017 The intersection graph of an orientable generic surface
Doron Ben Hadar
Algebr. Geom. Topol. 17(3): 1675-1700 (2017). DOI: 10.2140/agt.2017.17.1675

Abstract

The intersection graph M(i) of a generic surface i: F S3 is the set of values which are either singularities or intersections. It is a multigraph whose edges are transverse intersections of two surfaces and whose vertices are triple intersections and branch values. M(i) has an enhanced graph structure which Gui-Song Li referred to as a “daisy graph”. If F is oriented, then the orientation further refines the structure of M(i) into what Li called an “arrowed daisy graph”.

Li left open the question “which arrowed daisy graphs can be realized as the intersection graph of an oriented generic surface?” The main theorem of this article will answer this. I will also provide some generalizations and extensions to this theorem in Sections 4 and 5.

Citation

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Doron Ben Hadar. "The intersection graph of an orientable generic surface." Algebr. Geom. Topol. 17 (3) 1675 - 1700, 2017. https://doi.org/10.2140/agt.2017.17.1675

Information

Received: 20 January 2016; Accepted: 2 July 2016; Published: 2017
First available in Project Euclid: 16 November 2017

zbMATH: 1376.57019
MathSciNet: MR3677936
Digital Object Identifier: 10.2140/agt.2017.17.1675

Subjects:
Primary: 57N10, 57N12
Secondary: 57N35, 57N40, 57N75

Rights: Copyright © 2017 Mathematical Sciences Publishers

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Vol.17 • No. 3 • 2017
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