Determinacy - Revision history

en>Mean as custard: Reverted edits by Tuihjbnb (talk) to last version by Rjwilmsi

2014-12-13T11:10:08Z

Reverted edits by Tuihjbnb (talk) to last version by Rjwilmsi

← Older revision		Revision as of 13:10, 13 December 2014
Line 1:		Line 1:
	~~[[Image:Graph book sample.gif\|right]]~~		Andrew Simcox is the title his parents gave him and he totally loves this name. For many years he's been residing in Mississippi and he doesn't strategy on changing it. What me and my family adore is bungee leaping but I've been taking on new things lately. He is an information officer.<br><br>Here is my web-site: love psychic ([http://afeen.fbho.net/v2/index.php?do=/profile-210/info/ visit this web-site])
	~~In [[graph theory]], a '''book graph''' (often written <math>B_p</math> ) may be any of several kinds of graph.~~

	One kind, which may be called a '''quadrilateral book''', consists of ''p'' [[quadrilateral]]s sharing a common edge (known as the "spine" or "base" of the book).<ref>[http://mathworld.wolfram.com/BookGraph.html Eric W. Weisstein, "Book Graph."] From MathWorld–A Wolfram Web Resource.</ref> A book of this type is the ~~[[Cartesian product of graphs\|Cartesian product]] of a star~~ and ~~''K''<sub>2</sub> ~~.

	~~A second type, which might be called a~~ '~~''triangular book''', is the complete tripartite graph ''K''<sub>1,1,''p''</sub>. It is a graph consisting of <math>p</math> [[triangle]]~~s ~~sharing a common edge.<ref>Lingsheng Shi~~ and ~~Zhipeng Song, Upper bounds~~ on ~~the spectral radius of book-free and/or ''K''<sub>2,l</sub>-free graphs~~. ~~''Linear Algebra~~ and ~~its Applications~~'~~', vol~~. ~~420 (2007), pp. 526–529. {{doi\|10.1016/j.laa.2006.08.007}}</ref> A book of this type~~ is ~~a [[split graph]]~~.
	~~This graph has also been called a~~ <~~math~~>~~K_e(2,p)~~<~~/math~~>.<ref>{{cite journal\|last=Erdős\|first=Paul\|year=1963\|title=On the structure of linear graphs\|journal=Israel Journal of Mathematics\|volume=vol. 1\|pages=pp. 156–160\|authorlink=Paul Erdős\|doi=10.1007/BF02759702}}</ref>

	~~Given a graph <math>G</math>, one may write <math>bk(G)</math> for the largest book (of the kind being considered) contained within <math>G</math>.~~

	~~The term "book~~-graph" has been employed for other uses. Barioli<ref>Francesco Barioli, Completely positive matrices with a book-graph. ''Linear Algebra and its Applications'', vol. 277 (1998), pp. 11–31. {{doi\|10.1016/S0024-3795(97)10070-2}}</ref> used it to mean a graph composed of a number of arbitrary subgraphs having two vertices in common. (~~Barioli did not write <math>B_p</math> for his book-graph.)~~

	~~==Theorems on books==~~
	~~Denote the~~ [~~[Ramsey number]] of two (triangular) books by <math>r(B_p,\ B_q).<~~/~~math>~~

	* If <math>1\leq p\leq q</~~math>, then <math>r(B_p,\ B_q)=2q+3</math> (proved by [[Rousseau]] and [[Sheehan]])~~.

	* There exists a constant <math>c=o(1)</math> such that <math>r(B_p,\ B_q)=2q+3</math> whenever <math>q\geq cp</math>.
	* If <math> p\leq q/~~6+o(q)</math>, and <math>q</math> is large, the [[Ramsey number]] is given by <math>2q+3<~~/~~math>~~.

	* Let <math>C</math> be a constant, and <math>k = ~~Cn<~~/~~math>. Then every graph on <math>n<~~/~~math> vertices and <math>m<~~/~~math> edges contains a (triangular) <math>B_k</math>.<ref>P. Erdos, [http://projecteuclid.org/euclid.ijm/1255631811 On a theorem of Rademacher~~-~~Turán~~]~~. ''Illinois Journal of Mathematics'', vol. 6 (1962~~)~~, pp. 122–127.</ref>~~

	~~==References==~~
	~~{{Reflist}}~~

	~~{{DEFAULTSORT:Book (Graph Theory)}}~~
	~~[[Category:Parametric families of graphs]]~~
	~~[[Category:Planar graphs]]~~

en>Monkbot: /* Games of imperfect information */Fix CS1 deprecated date parameter errors

2014-01-16T16:47:19Z

Games of imperfect information: Fix CS1 deprecated date parameter errors

← Older revision		Revision as of 18:47, 16 January 2014
Line 1:		Line 1:
	~~Hi there~~. ~~Allow me begin~~ [http://~~www~~.~~neweracinema~~.com/~~tube~~/~~user~~/~~D69E visit these guys] by introducing~~ the ~~writer~~, ~~her title~~ [~~http:~~//~~www~~.~~pathwayschico~~.~~org~~/~~blogs~~/~~post~~/~~216965 std testing at home] is Myrtle Cleary~~. ~~He is truly fond~~ of ~~performing ceramics but~~ ~~std testing at home he is~~ having [~~http:~~//~~whatdoesgenitalherpeslook.tumblr.com difficulties~~] to [~~http:~~//~~faststdtestlabs~~.~~com~~/ ~~discover time~~] ~~for it~~. ~~For years he's been working as~~ a ~~receptionist. California is our birth location~~.<br><br>~~std home test Take~~ a ~~look at my site - at home std test [~~[http://~~www~~.~~crmidol~~.~~com~~/~~discussion~~/~~19701/how-tell-if-woman-interested-or-sexually-captivated-you simply click the following internet page~~]]		[[Image:Graph book sample.gif\|right]]
			In [[graph theory]], a '''book graph''' (often written <math>B_p</math> ) may be any of several kinds of graph.

			One kind, which may be called a '''quadrilateral book''', consists of ''p'' [[quadrilateral]]s sharing a common edge (known as the "spine" or "base" of the book).<ref>[http://mathworld.wolfram.com/BookGraph.html Eric W. Weisstein, "Book Graph."] From MathWorld–A Wolfram Web Resource.</ref> A book of this type is the [[Cartesian product of graphs\|Cartesian product]] of a star and ''K''<sub>2</sub> .

			A second type, which might be called a '''triangular book''', is the complete tripartite graph ''K''<sub>1,1,''p''</sub>. It is a graph consisting of <math>p</math> [[triangle]]s sharing a common edge.<ref>Lingsheng Shi and Zhipeng Song, Upper bounds on the spectral radius of book-free and/or ''K''<sub>2,l</sub>-free graphs. ''Linear Algebra and its Applications'', vol. 420 (2007), pp. 526–529. {{doi\|10.1016/j.laa.2006.08.007}}</ref> A book of this type is a [[split graph]].
			This graph has also been called a <math>K_e(2,p)</math>.<ref>{{cite journal\|last=Erdős\|first=Paul\|year=1963\|title=On the structure of linear graphs\|journal=Israel Journal of Mathematics\|volume=vol. 1\|pages=pp. 156–160\|authorlink=Paul Erdős\|doi=10.1007/BF02759702}}</ref>

			Given a graph <math>G</math>, one may write <math>bk(G)</math> for the largest book (of the kind being considered) contained within <math>G</math>.

			The term "book-graph" has been employed for other uses. Barioli<ref>Francesco Barioli, Completely positive matrices with a book-graph. ''Linear Algebra and its Applications'', vol. 277 (1998), pp. 11–31. {{doi\|10.1016/S0024-3795(97)10070-2}}</ref> used it to mean a graph composed of a number of arbitrary subgraphs having two vertices in common. (Barioli did not write <math>B_p</math> for his book-graph.)

			==Theorems on books==
			Denote the [[Ramsey number]] of two (triangular) books by <math>r(B_p,\ B_q).</math>

			* If <math>1\leq p\leq q</math>, then <math>r(B_p,\ B_q)=2q+3</math> (proved by [[Rousseau]] and [[Sheehan]]).

			* There exists a constant <math>c=o(1)</math> such that <math>r(B_p,\ B_q)=2q+3</math> whenever <math>q\geq cp</math>.
			* If <math> p\leq q/6+o(q)</math>, and <math>q</math> is large, the [[Ramsey number]] is given by <math>2q+3</math>.

			* Let <math>C</math> be a constant, and <math>k = Cn</math>. Then every graph on <math>n</math> vertices and <math>m</math> edges contains a (triangular) <math>B_k</math>.<ref>P. Erdos, [http://projecteuclid.org/euclid.ijm/1255631811 On a theorem of Rademacher-Turán]. ''Illinois Journal of Mathematics'', vol. 6 (1962), pp. 122–127.</ref>

			==References==
			{{Reflist}}

			{{DEFAULTSORT:Book (Graph Theory)}}
			[[Category:Parametric families of graphs]]
			[[Category:Planar graphs]]

24.117.169.245: /* Woodin cardinals */ used $...$ format for sub-superscripts

2012-04-22T01:22:50Z

Woodin cardinals: used <math>...</math> format for sub-superscripts

New page

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Determinacy - Revision history

en>Mean as custard: Reverted edits by Tuihjbnb (talk) to last version by Rjwilmsi

en>Monkbot: /* Games of imperfect information */Fix CS1 deprecated date parameter errors

24.117.169.245: /* Woodin cardinals */ used ... format for sub-superscripts

24.117.169.245: /* Woodin cardinals */ used $...$ format for sub-superscripts