Analytic polyhedron - Revision history

en>Daniele.tampieri: Added a reference and corrected a citation: the contribution on Weil polyhedron is in Kenkin's article, not in Chirka's one.

2014-12-08T09:39:27Z

Added a reference and corrected a citation: the contribution on Weil polyhedron is in Kenkin's article, not in Chirka's one.

← Older revision		Revision as of 11:39, 8 December 2014
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	~~In [[extremal graph theory]], the '''forbidden subgraph problem'''~~ is the following problem: given a graph ''G'', find the maximal number of edges in an ''n''-vertex graph which does not have a [[Glossary of graph theory#Subgraphs\|subgraph]] [[graph isomorphism\|isomorphic]] to ~~''G''. In this context, ''G'' is called a '''forbidden subgraph'''~~. <~~ref name=bollobas~~>~~''Combinatorics: Set Systems, Hypergraphs, Families~~ of ~~Vectors and Probabilistic Combinatorics'', [[Béla Bollobás]], 1986, ISBN 0-521-33703-8, [http://books~~.~~google~~.com/books?id=LUUrTJ1Cx_0C&pg=PA53&lpg=PA53&dq=%22forbidden+subgraph+problem%22&source=bl&ots=o_ZcOV93Ep&sig=70mXvYYMHyDSGdmOIwpHMLpx86E&hl=en&ei=n3KjSfHMCInOsAOCttieAg&sa=X&oi=book_result&resnum=7&ct=result#PPA54,M1 p. 53, 54]<~~/ref~~>		There is nothing to tell about me I think.<br>Yes! Im a member of wmflabs.org.<br>I really hope I'm useful at all<br><br>Here is my web site ... [http://www.natwestconstructions.com/brand/coach.asp?Topic=15 authentic coach outlet online]

	It is also called the '''Turán-type problem''' and the corresponding number is called the '''Turán number for graph''' ''G''. It is called so in memory of [[Pál Turán]], who determined this number for all ''n'' ~~and~~ all ~~[[complete graph]]s~~ <~~math~~>~~K_r,\, n\geq r \geq 3~~<~~/math~~>. ~~<ref>[http://books~~.~~google.com/books?id=4hWxnsLIfVAC&pg=PA254&dq=%22Turan-type+problem%22&lr= p~~. ~~254]</ref>~~

	~~An equivalent problem is how many edges in an ''n''-vertex graph guarantee that it has a subgraph isomorphic to ''G''?<ref>"Modern Graph Theory", by Béla Bollobás, 1998, ISBN 0-387-98488-7,~~ [http://~~books~~.~~google~~.com/~~books?id=SbZKSZ-1qrwC&pg=PA123&dq=%22forbidden+subgraph+problem%22&lr=#PPA103,M1 p. 103]<~~/~~ref>~~

	~~The problem may be generalized for a set of forbidden subgraphs ''S'': find the maximal number of edges in an ''n''-vertex graph which does not have a subgraph isomorphic to any graph fom ''S''~~.~~<ref>Handbook of Discrete and Combinatorial Mathematics By Kenneth H. Rosen, John G. Michaels [http://books.google.com/books~~?~~id=C3tJsmWRQvkC&pg=PA590&dq~~=~~%22turan+number%22#PPA590,M1 p. 590]</ref>~~

	~~==See also==~~
	*[[Turán number]]
	*[[Subgraph isomorphism problem]]
	*[[Forbidden graph characterization]]
	*[[Zarankiewicz problem]]

	~~==References==~~
	~~{{reflist}}~~

	~~{{combin-stub}}~~
	~~[[Category:Extremal graph theory]~~]

en>Mark viking: Added boundary and a better definition of the Weil domain/polyhedron + ref verifying

2013-09-30T08:47:38Z

Added boundary and a better definition of the Weil domain/polyhedron + ref verifying

← Older revision		Revision as of 10:47, 30 September 2013
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			It is also called the '''Turán-type problem''' and the corresponding number is called the '''Turán number for graph''' ''G''. It is called so in memory of [[Pál Turán]], who determined this number for all ''n'' and all [[complete graph]]s <math>K_r,\, n\geq r \geq 3</math>. <ref>[http://books.google.com/books?id=4hWxnsLIfVAC&pg=PA254&dq=%22Turan-type+problem%22&lr= p. 254]</ref>

			An equivalent problem is how many edges in an ''n''-vertex graph guarantee that it has a subgraph isomorphic to ''G''?<ref>"Modern Graph Theory", by Béla Bollobás, 1998, ISBN 0-387-98488-7, [http://books.google.com/books?id=SbZKSZ-1qrwC&pg=PA123&dq=%22forbidden+subgraph+problem%22&lr=#PPA103,M1 p. 103]</ref>

			The problem may be generalized for a set of forbidden subgraphs ''S'': find the maximal number of edges in an ''n''-vertex graph which does not have a subgraph isomorphic to any graph fom ''S''.<ref>Handbook of Discrete and Combinatorial Mathematics By Kenneth H. Rosen, John G. Michaels [http://books.google.com/books?id=C3tJsmWRQvkC&pg=PA590&dq=%22turan+number%22#PPA590,M1 p. 590]</ref>

			==See also==
			*[[Turán number]]
			*[[Subgraph isomorphism problem]]
			*[[Forbidden graph characterization]]
			*[[Zarankiewicz problem]]

			==References==
			{{reflist}}

			{{combin-stub}}
			[[Category:Extremal graph theory]]

en>David Eppstein: stub sort

2012-08-29T07:18:40Z

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