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1-Factorization of K 2n - История изменений
2024-03-28T10:01:31Z
История изменений этой страницы в вики
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http://pco.iis.nsk.su/grapp/index.php?title=1-Factorization_of_K_2n&diff=10778&oldid=prev
ALEXM в 06:58, 24 сентября 2018
2018-09-24T06:58:17Z
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Предыдущая версия</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Версия от 13:58, 24 сентября 2018</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l6">Строка 6:</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>distinct one-factors forms a Hamiltonian cycle of <math>K_{2n}</math>. P1Fs of</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>distinct one-factors forms a Hamiltonian cycle of <math>K_{2n}</math>. P1Fs of</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><math>K_{2n}</math> are known to exist when <math>2n-1</math> or <math>n</math> is prime, and for <math>2n</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><math>K_{2n}</math> are known to exist when <math>2n-1</math> or <math>n</math> is prime, and for <math>2n</div></td></tr>
<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>\in \{16, 28, 36,40, 50, 126, 170, 244, 344, 730, <del style="font-weight: bold; text-decoration: none;">\\ </del>1332, 1370, 1850,</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>\in \{16, 28, 36,40, 50, 126, 170, 244, 344, 730, 1332, 1370, 1850,</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>2198, 3126, 6860, 12168, 16808, 29792\}</math>.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>2198, 3126, 6860, 12168, 16808, 29792\}</math>.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>It has been conjectured that</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>It has been conjectured that</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>a perfect one-factorization of <math>K_{2n}</math> exists for all <math>n \geq 2</math>.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>a perfect one-factorization of <math>K_{2n}</math> exists for all <math>n \geq 2</math>.</div></td></tr>
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ALEXM
http://pco.iis.nsk.su/grapp/index.php?title=1-Factorization_of_K_2n&diff=7243&oldid=prev
Glk: Новая страница: «'''1-Factorization of <math>K_{2n}</math>''' --- один-факторизация графа <math>K_{2n}</math>. A '''one-factorization''' of <math>K_{2n}</math>…»
2011-04-27T07:52:50Z
<p>Новая страница: «'''1-Factorization of <math>K_{2n}</math>''' --- один-факторизация графа <math>K_{2n}</math>. A '''one-factorization''' of <math>K_{2n}</math>…»</p>
<p><b>Новая страница</b></p><div>'''1-Factorization of <math>K_{2n}</math>''' --- один-факторизация графа<br />
<math>K_{2n}</math>. <br />
<br />
A '''one-factorization''' of <math>K_{2n}</math> is a partition of the edge-set<br />
of <math>K_{2n}</math> into <math>2n-1</math> ''one-factors''. A '''perfect one-factorization (P1F)''' is a one-factorization in which every pair of<br />
distinct one-factors forms a Hamiltonian cycle of <math>K_{2n}</math>. P1Fs of<br />
<math>K_{2n}</math> are known to exist when <math>2n-1</math> or <math>n</math> is prime, and for <math>2n<br />
\in \{16, 28, 36,40, 50, 126, 170, 244, 344, 730, \\ 1332, 1370, 1850,<br />
2198, 3126, 6860, 12168, 16808, 29792\}</math>.<br />
<br />
It has been conjectured that<br />
a perfect one-factorization of <math>K_{2n}</math> exists for all <math>n \geq 2</math>.</div>
Glk