Simple Graphs as Simplicial Complexes: the Mycielskian of a Graph

Pole DC	Wartość	Język
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

Pliki w tej pozycji:

Plik	Opis	Rozmiar	Format
v10037-012-0019-8.pdf		289,06 kB	Adobe PDF	Otwórz

Pokaż uproszczony widok rekordu Zobacz statystyki

Pozycja ta dostępna jest na podstawie licencji Licencja Creative Commons CCL