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http://hdl.handle.net/11320/3639
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Pole DC | Wartość | Język |
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dc.contributor.author | Rudnicki, Piotr | - |
dc.contributor.author | Stewart, Lorna | - |
dc.date.accessioned | 2015-12-06T19:05:35Z | - |
dc.date.available | 2015-12-06T19:05:35Z | - |
dc.date.issued | 2012 | - |
dc.identifier.citation | Formalized Mathematics, Volume 20, Issue 2, 2012, Pages 161-174 | - |
dc.identifier.issn | 1426-2630 | - |
dc.identifier.issn | 1898-9934 | - |
dc.identifier.uri | http://hdl.handle.net/11320/3639 | - |
dc.description.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]. | - |
dc.description.sponsorship | This work has been partially supported by the NSERC grant OGP 9207 | - |
dc.language.iso | en | - |
dc.publisher | De Gruyter Open | - |
dc.title | Simple Graphs as Simplicial Complexes: the Mycielskian of a Graph | - |
dc.type | Article | - |
dc.identifier.doi | 10.2478/v10037-012-0019-8 | - |
dc.description.Affiliation | Rudnicki Piotr - University of Alberta, Edmonton, Canada | - |
dc.description.Affiliation | Stewart Lorna - University of Alberta, Edmonton, Canada | - |
dc.description.references | Grzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377-382, 1990. | - |
dc.description.references | Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990. | - |
dc.description.references | Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990. | - |
dc.description.references | Grzegorz Bancerek. Tarski’s classes and ranks. Formalized Mathematics, 1(3):563-567, 1990. | - |
dc.description.references | Grzegorz Bancerek. Mizar analysis of algorithms: Preliminaries. Formalized Mathematics, 15(3):87-110, 2007, doi:10.2478/v10037-007-0011-x. | - |
dc.description.references | Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990. | - |
dc.description.references | Czesław Bylinski. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990. | - |
dc.description.references | Czesław Bylinski. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990. | - |
dc.description.references | Agata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165-167, 1990. | - |
dc.description.references | Frank Harary. Graph theory. Addison-Wesley, 1969. | - |
dc.description.references | Rafał Kwiatek. Factorial and Newton coefficients. Formalized Mathematics, 1(5):887-890, 1990. | - |
dc.description.references | J. Mycielski. Sur le coloriage des graphes. Colloquium Mathematicum, 3:161-162, 1955. | - |
dc.description.references | Beata Padlewska. Families of sets. Formalized Mathematics, 1(1):147-152, 1990. | - |
dc.description.references | Konrad Raczkowski and Paweł Sadowski. Equivalence relations and classes of abstraction. Formalized Mathematics, 1(3):441-444, 1990. | - |
dc.description.references | Piotr Rudnicki and Lorna Stewart. The Mycielskian of a graph. Formalized Mathematics, 19(1):27-34, 2011, doi: 10.2478/v10037-011-0005-6. | - |
dc.description.references | Andrzej Trybulec. Enumerated sets. Formalized Mathematics, 1(1):25-34, 1990. | - |
dc.description.references | Andrzej Trybulec. Many sorted sets. Formalized Mathematics, 4(1):15-22, 1993. | - |
dc.description.references | Andrzej Trybulec and Agata Darmochwał. Boolean domains. Formalized Mathematics, 1(1):187-190, 1990. | - |
dc.description.references | Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990. | - |
dc.description.references | Oswald Veblen. Analysis Situs, volume V. AMS Colloquium Publications, 1931 | - |
Występuje w kolekcji(ach): | Formalized Mathematics, 2012, Volume 20, Issue 2 |
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v10037-012-0019-8.pdf | 289,06 kB | Adobe PDF | Otwórz |
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