Ordinal optimization - Revision history

en>Makyen: Fix various citation errors/issues: "unknown parameter", ISBN, LCCN, URL, simple coauthors (deprecated), simple author-link, etc. Replace hard space per WP:NBSP. Run gen fixes and typos if any found. using AWB

2014-05-04T05:26:00Z

Fix various citation errors/issues: "unknown parameter", ISBN, LCCN, URL, simple coauthors (deprecated), simple author-link, etc. Replace hard space per WP:NBSP. Run gen fixes and typos if any found. using AWB

← Older revision		Revision as of 07:26, 4 May 2014
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	~~In [[graph theory]],~~ the '~~''Edmonds matrix''' <math>A</math>~~ of a balanced [[bipartite graph]] <math>G(U, V, E)</math> with [[Set (mathematics)\|set]]s of vertices <math>U = \{u_1, u_2, \dots , u_n \}</math> and <math>V = \{v_1, v_2, \dots , v_n\}</math> is defined by		Royal Votaw is my title but I never truly favored that name. Bottle tops gathering is the only pastime his wife doesn't approve of. I presently reside in Arizona but now I'm contemplating other choices. Interviewing is how I make a residing and it's some thing I truly enjoy.<br><br>Also visit my site - [http://brazil.amor-amore.com/nilindon car warranty]

	~~:<math> A_{ij} = \left\{ \begin{array}{ll}~~
	~~x_{ij} & (u_i, v_j) \~~in ~~E \\~~
	~~0 & (u_i, v_j) \notin E~~
	~~\end{array}\right.</math>~~

	~~where the '~~'~~x''<sub>ij</sub> are indeterminates~~. ~~One application of the Edmonds matrix of a bipartite graph~~ is ~~that the graph admits~~ a ~~[[perfect matching]] if~~ and ~~only if the polynomial det(''A'~~'<~~sub~~>ij<~~/sub~~>) in the ''x''<sub>ij</sub> is not identically zero. Furthermore, the number of perfect matchings is equal to the number of [[monomials]] in the polynomial det(''A''), and is also equal to the [[permanent]] of ''A''.

	~~The Edmonds matrix is named after [~~[~~Jack Edmonds]]. The [[Tutte matrix]] is a generalisation to non-bipartite graphs.~~

	~~==References==~~
	*{{cite book\|author=R. Motwani, P. Raghavan \|title=Randomized Algorithms \|url=http://~~books~~.~~google~~.com/~~books/cambridge?id=QKVY4mDivBEC&pg=PR5&sig=8KZG5MvVdHKKRcLYdN91fGyIrBQ#PPA167,M1 \|publisher=Cambridge University Press\|year=1995\|page=167}}~~
	*{{cite book\|author=Allen B. Tucker\|title=Computer Science Handbook\|publisher=CRC Press\|date=2004\|isbn=1-58488-360-X\|page=12.19}}

	~~{{combin-stub}}~~
	~~[[Category:Graph theory objects]]~~
	~~[[Category:Matrices]~~]

en>Rjwilmsi: Citation parameter fixes, using AWB

2013-09-30T11:58:11Z

Citation parameter fixes, using AWB

← Older revision		Revision as of 13:58, 30 September 2013
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	~~The name~~ of ~~the author~~ is ~~Nestor~~. ~~Meter reading is exactly~~ where ~~my primary income arrives from but soon I~~'~~ll be on my personal~~. I'~~ve always cherished residing~~ in ~~Idaho~~. ~~To perform handball~~ is the ~~thing she enjoys most~~ of ~~all~~.~~<br><br>my web site ::~~ [http://~~beta~~.~~Westernstatesfireequipment~~.com/~~ActivityFeed~~/~~MyProfile/tabid/93/userId/1095/Default~~.~~aspx auto warranty~~]		In [[graph theory]], the '''Edmonds matrix''' <math>A</math> of a balanced [[bipartite graph]] <math>G(U, V, E)</math> with [[Set (mathematics)\|set]]s of vertices <math>U = \{u_1, u_2, \dots , u_n \}</math> and <math>V = \{v_1, v_2, \dots , v_n\}</math> is defined by

			:<math> A_{ij} = \left\{ \begin{array}{ll}
			x_{ij} & (u_i, v_j) \in E \\
			0 & (u_i, v_j) \notin E
			\end{array}\right.</math>

			where the ''x''<sub>ij</sub> are indeterminates. One application of the Edmonds matrix of a bipartite graph is that the graph admits a [[perfect matching]] if and only if the polynomial det(''A''<sub>ij</sub>) in the ''x''<sub>ij</sub> is not identically zero. Furthermore, the number of perfect matchings is equal to the number of [[monomials]] in the polynomial det(''A''), and is also equal to the [[permanent]] of ''A''.

			The Edmonds matrix is named after [[Jack Edmonds]]. The [[Tutte matrix]] is a generalisation to non-bipartite graphs.

			==References==
			*{{cite book\|author=R. Motwani, P. Raghavan \|title=Randomized Algorithms \|url=http://books.google.com/books/cambridge?id=QKVY4mDivBEC&pg=PR5&sig=8KZG5MvVdHKKRcLYdN91fGyIrBQ#PPA167,M1 \|publisher=Cambridge University Press\|year=1995\|page=167}}
			*{{cite book\|author=Allen B. Tucker\|title=Computer Science Handbook\|publisher=CRC Press\|date=2004\|isbn=1-58488-360-X\|page=12.19}}

			{{combin-stub}}
			[[Category:Graph theory objects]]
			[[Category:Matrices]]

en>SchreiberBike: Repairing links to disambiguation pages - You can help! - Lattice

2012-05-23T02:32:18Z

Repairing links to disambiguation pages - You can help! - Lattice

New page

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