A Short Proof of Euler–Poincaré Formula

HLINĚNÝ, Petr. A Short Proof of Euler–Poincaré Formula. In Nešetřil J., Perarnau G., Rué J., Serra O. Extended Abstracts EuroComb 2021. Trends in Mathematics. Cham: Birkhäuser, 2021, p. 92-96. ISBN 978-3-030-83822-5. Available from: https://dx.doi.org/10.1007/978-3-030-83823-2_15.

Basic information

Original name

A Short Proof of Euler–Poincaré Formula

Authors

HLINĚNÝ, Petr (203 Czech Republic, guarantor, belonging to the institution)

Edition

Cham, Extended Abstracts EuroComb 2021. Trends in Mathematics, p. 92-96, 5 pp. 2021

Publisher

Birkhäuser

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Other information

Language

English

Type of outcome

Stať ve sborníku

Field of Study

10201 Computer sciences, information science, bioinformatics

Country of publisher

Switzerland

Confidentiality degree

není předmětem státního či obchodního tajemství

Publication form

printed version "print"

References:

URL

RIV identification code

RIV/00216224:14330/21:00119291

Organization unit

Faculty of Informatics

ISBN

978-3-030-83822-5

ISSN

DOI

http://dx.doi.org/10.1007/978-3-030-83823-2_15

Keywords in English

Euler–Poincaré formula; Polytopes; Discharging

Tags

formela-conference

Tags

International impact, Reviewed

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Abstract

V originále

"V-E+F=2", the famous Euler’s polyhedral formula, has a natural generalization to convex polytopes in every finite dimension, also known as the Euler-Poincaré Formula. We provide another short inductive combinatorial proof of the general formula. Our proof is self-contained and it does not use shellability of polytopes.

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Links

GA20-04567S, research and development project

Name: Struktura efektivně řešitelných případů těžkých algoritmických problémů na grafech Investor: Czech Science Foundation