Simple Graphs as Simplicial Complexes: the Mycielskian of a Graph

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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].

Keywords:
References
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Formalized Mathematics

(a computer assisted approach)

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SCImago Journal Rank (SJR) 2016: 0.207
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researchers in the fields of formal methods and computer-checked mathematics

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