Simple Graphs as Simplicial Complexes: the Mycielskian of a Graph

Piotr Rudnicki; Lorna Stewart

Formalized Mathematics (2012)

  • Volume: 20, Issue: 2, page 161-174
  • ISSN: 1426-2630

Abstract

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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].

How to cite

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Piotr Rudnicki, and Lorna Stewart. "Simple Graphs as Simplicial Complexes: the Mycielskian of a Graph." Formalized Mathematics 20.2 (2012): 161-174. <http://eudml.org/doc/267612>.

@article{PiotrRudnicki2012,
abstract = {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].},
author = {Piotr Rudnicki, Lorna Stewart},
journal = {Formalized Mathematics},
keywords = {clique number; chromatic number; Mycielskian},
language = {eng},
number = {2},
pages = {161-174},
title = {Simple Graphs as Simplicial Complexes: the Mycielskian of a Graph},
url = {http://eudml.org/doc/267612},
volume = {20},
year = {2012},
}

TY - JOUR
AU - Piotr Rudnicki
AU - Lorna Stewart
TI - Simple Graphs as Simplicial Complexes: the Mycielskian of a Graph
JO - Formalized Mathematics
PY - 2012
VL - 20
IS - 2
SP - 161
EP - 174
AB - 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].
LA - eng
KW - clique number; chromatic number; Mycielskian
UR - http://eudml.org/doc/267612
ER -

References

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