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Expansive - Revision history
2026-05-21T23:13:02Z
Revision history for this page on the wiki
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https://en.formulasearchengine.com/index.php?title=Expansive&diff=14142&oldid=prev
en>Squids and Chips: WPCleaner v1.27 - Repaired 1 link to disambiguation page - (You can help) - Rigid
2013-05-22T21:38:48Z
<p><a href="/index.php?title=En:WP:CLEANER&action=edit&redlink=1" class="new" title="En:WP:CLEANER (page does not exist)">WPCleaner</a> v1.27 - Repaired 1 link to disambiguation page - <a href="/index.php?title=WP:DPL&action=edit&redlink=1" class="new" title="WP:DPL (page does not exist)">(You can help)</a> - <a href="/index.php?title=Rigid&action=edit&redlink=1" class="new" title="Rigid (page does not exist)">Rigid</a></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 23:38, 22 May 2013</td>
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<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">Hi there, I am Andrew Berryhill. To play lacross </del>is the <del style="font-weight: bold; text-decoration: none;">factor I adore most </del>of <del style="font-weight: bold; text-decoration: none;">all</del>. <del style="font-weight: bold; text-decoration: none;">I am an invoicing officer </del>and <del style="font-weight: bold; text-decoration: none;">I</del>'<del style="font-weight: bold; text-decoration: none;">ll be promoted soon. I</del>'<del style="font-weight: bold; text-decoration: none;">ve always cherished residing </del>in <del style="font-weight: bold; text-decoration: none;">Kentucky but now I'm considering other choices.</del><<del style="font-weight: bold; text-decoration: none;">br</del>><<del style="font-weight: bold; text-decoration: none;">br</del>><del style="font-weight: bold; text-decoration: none;">my blog post: free psychic readings </del>([<del style="font-weight: bold; text-decoration: none;">http://checkmates</del>.<del style="font-weight: bold; text-decoration: none;">co</del>.<del style="font-weight: bold; text-decoration: none;">za</del>/<del style="font-weight: bold; text-decoration: none;">index</del>.<del style="font-weight: bold; text-decoration: none;">php?do</del>=/<del style="font-weight: bold; text-decoration: none;">profile-56347</del>/<del style="font-weight: bold; text-decoration: none;">info</del>/ <del style="font-weight: bold; text-decoration: none;">http:</del>//<del style="font-weight: bold; text-decoration: none;">checkmates</del>.<del style="font-weight: bold; text-decoration: none;">co</del>.<del style="font-weight: bold; text-decoration: none;">za</del>/<del style="font-weight: bold; text-decoration: none;">index</del>.<del style="font-weight: bold; text-decoration: none;">php?do</del>=/<del style="font-weight: bold; text-decoration: none;">profile-56347/info</del>]<del style="font-weight: bold; text-decoration: none;">)</del></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">The '''Symmetric hypergraph theorem''' </ins>is <ins style="font-weight: bold; text-decoration: none;">a theorem in [[combinatorics]] that puts an upper bound on </ins>the <ins style="font-weight: bold; text-decoration: none;">[[Graph coloring#Chromatic number|chromatic number]] </ins>of <ins style="font-weight: bold; text-decoration: none;">a [[Graph (mathematics)|graph]] (or [[hypergraph]] in general)</ins>. <ins style="font-weight: bold; text-decoration: none;"> The original reference for this paper is unknown at the moment, </ins>and <ins style="font-weight: bold; text-decoration: none;">has been called folklore.<ref>R. Graham, B. Rothschild, J. Spencer. Ramsey Theory. 2nd ed., Wiley, New-York, 1990.</ref></ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">==Statement==</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">A [[Group (mathematics)|group]] <math>G</math> [[group action|acting on a set]] <math>S</math> is called ''[[Group action#Types of actions|transitive]]</ins>'' <ins style="font-weight: bold; text-decoration: none;">if given any two elements <math>x</math> and <math>y</math> </ins>in <<ins style="font-weight: bold; text-decoration: none;">math>S</math>, there exists an element <math>f</math> of <math>G</math> such that <math</ins>><ins style="font-weight: bold; text-decoration: none;">f(x) = y</ins><<ins style="font-weight: bold; text-decoration: none;">/math</ins>><ins style="font-weight: bold; text-decoration: none;">. A graph </ins>(<ins style="font-weight: bold; text-decoration: none;">or hypergraph) is called ''symmetric'' if it's </ins>[<ins style="font-weight: bold; text-decoration: none;">[automorphism group]] is transitive</ins>.</div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">'''Theorem</ins>.<ins style="font-weight: bold; text-decoration: none;">''' Let <math>H = (S, E)<</ins>/<ins style="font-weight: bold; text-decoration: none;">math> be a symmetric hypergraph</ins>. <ins style="font-weight: bold; text-decoration: none;"> Let <math>m </ins>= <ins style="font-weight: bold; text-decoration: none;">|S|<</ins>/<ins style="font-weight: bold; text-decoration: none;">math>, and let <math>\chi(H)<</ins>/<ins style="font-weight: bold; text-decoration: none;">math> denote the chromatic number of <math>H<</ins>/<ins style="font-weight: bold; text-decoration: none;">math>, and let <math>\alpha(H)<</ins>/<ins style="font-weight: bold; text-decoration: none;">math> denote the [[Glossary of graph theory#Independence|independence number]] of <math>H<</ins>/<ins style="font-weight: bold; text-decoration: none;">math></ins>. <ins style="font-weight: bold; text-decoration: none;"> Then </ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"><center><math>\chi(H) < 1 + \frac{m}{\alpha(H)}\ln m</ins>.<ins style="font-weight: bold; text-decoration: none;"></math><</ins>/<ins style="font-weight: bold; text-decoration: none;">center></ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">==Applications==</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">This theorem has applications to [[Ramsey theory]], specifically [[graph Ramsey theory]]</ins>. <ins style="font-weight: bold; text-decoration: none;"> Using this theorem, a relationship between the graph Ramsey numbers and the extremal numbers can be shown (see Graham-Rothschild-Spencer for the details).</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">==See also==</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">* [[Ramsey theory]]</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">==Notes=</ins>=</div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"><references</ins>/<ins style="font-weight: bold; text-decoration: none;">></ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">[[Category:Graph coloring]]</ins></div></td></tr>
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en>Squids and Chips
https://en.formulasearchengine.com/index.php?title=Expansive&diff=249045&oldid=prev
en>777sms at 03:52, 14 April 2012
2012-04-14T03:52:48Z
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<p><b>New page</b></p><div>Hi there, I am Andrew Berryhill. To play lacross is the factor I adore most of all. I am an invoicing officer and I'll be promoted soon. I've always cherished residing in Kentucky but now I'm considering other choices.<br><br>my blog post: free psychic readings ([http://checkmates.co.za/index.php?do=/profile-56347/info/ http://checkmates.co.za/index.php?do=/profile-56347/info])</div>
en>777sms