# Simple Graphs as Simplicial Complexes: the Mycielskian of a Graph

Formalized Mathematics (2012)

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

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topPiotr 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 -

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