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].
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2019 ◽
Vol 76
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pp. 53-61
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1976 ◽
Vol 28
(6)
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pp. 1340-1344
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2020 ◽
Vol 140
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pp. 84-97
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1986 ◽
Vol 100
(2)
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pp. 303-317
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2014 ◽
Vol 105
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pp. 6-10
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