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Formalized Mathematics

(a computer assisted approach)

Editor-in-Chief: Matuszewski, Roman

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1898-9934
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Volume 20, Issue 2 (Dec 2012)

Issues

Simple Graphs as Simplicial Complexes: the Mycielskian of a Graph

Piotr Rudnicki
  • University of Alberta, Edmonton, Canada
/ Lorna Stewart
  • University of Alberta, Edmonton, Canada
Published Online: 2013-02-02 | DOI: https://doi.org/10.2478/v10037-012-0019-8

Summary

Harary [10, p. 7] claims that Veblen [20, p. 2] first suggested to formalize simple graphs using simplicial complexes. We have developed basic terminology for simple graphs as at most 1-dimensional complexes.

We formalize this new setting and then reprove Mycielski’s [12] construction resulting in a triangle-free graph with arbitrarily large chromatic number. A different formalization of similar material is in [15].

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  • [20] Oswald Veblen. Analysis Situs, volume V. AMS Colloquium Publications, 1931

About the article

This work has been partially supported by the NSERC grant OGP 9207


Published Online: 2013-02-02

Published in Print: 2012-12-01


Citation Information: Formalized Mathematics, ISSN (Online) 1898-9934, ISSN (Print) 1426-2630, DOI: https://doi.org/10.2478/v10037-012-0019-8. Export Citation

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[1]
Josef Urban, Piotr Rudnicki, and Geoff Sutcliffe
Journal of Automated Reasoning, 2013, Volume 50, Number 2, Page 229

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