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Counterexample to the Hanani-Tutte theorem on the surface of genus 4 Kyncl, Jan

Description

We find a graph of genus 5 and its drawing on the orientable surface of genus 4 with every pair of independent edges crossing an even number of times. This shows that the strong Hanani-Tutte theorem cannot be generalized to the orientable surface of genus 4. As a base step in the construction we use a counterexample to the unified Hanani-Tutte theorem on the torus. The result was obtained together with Radoslav Fulek.

Item Metadata

Title
Counterexample to the Hanani-Tutte theorem on the surface of genus 4
Creator
Kyncl, Jan
Publisher
Banff International Research Station for Mathematical Innovation and Discovery
Date Issued
2017-08-22T14:58
Description
We find a graph of genus 5 and its drawing on the orientable surface of genus 4 with every pair of independent edges crossing an even number of times. This shows that the strong Hanani-Tutte theorem cannot be generalized to the orientable surface of genus 4. As a base step in the construction we use a counterexample to the unified Hanani-Tutte theorem on the torus. The result was obtained together with Radoslav Fulek.
Extent
20 minutes
Subject
Mathematics; Combinatorics; Computer science; Discrete mathematics
Type
Moving Image
File Format
video/mp4
Language
eng
Notes
Author affiliation: Charles University
Series
BIRS Workshop Lecture Videos (Banff, Alta)
Date Available
2018-04-09
Provider
Vancouver : University of British Columbia Library
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International
DOI
10.14288/1.0365302
URI
http://hdl.handle.net/2429/65254
Affiliation
Non UBC
Peer Review Status
Unreviewed
Scholarly Level
Faculty
Rights URI
http://creativecommons.org/licenses/by-nc-nd/4.0/
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Attribution-NonCommercial-NoDerivatives 4.0 International