http://pco.iis.nsk.su/grapp/index.php?title=1-Factorization_of_K_2n&feed=atom&action=history 1-Factorization of K 2n - История изменений 2024-03-28T10:01:31Z История изменений этой страницы в вики MediaWiki 1.39.3 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 <p></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="ru"> <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> <td colspan="2" class="diff-lineno">Строка 6:</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>distinct one-factors forms a Hamiltonian cycle of &lt;math&gt;K_{2n}&lt;/math&gt;. 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 &lt;math&gt;K_{2n}&lt;/math&gt;. 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>&lt;math&gt;K_{2n}&lt;/math&gt; are known to exist when &lt;math&gt;2n-1&lt;/math&gt; or &lt;math&gt;n&lt;/math&gt; is prime, and for &lt;math&gt;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>&lt;math&gt;K_{2n}&lt;/math&gt; are known to exist when &lt;math&gt;2n-1&lt;/math&gt; or &lt;math&gt;n&lt;/math&gt; is prime, and for &lt;math&gt;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\}&lt;/math&gt;.</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\}&lt;/math&gt;.</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 &lt;math&gt;K_{2n}&lt;/math&gt; exists for all &lt;math&gt;n \geq 2&lt;/math&gt;.</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 &lt;math&gt;K_{2n}&lt;/math&gt; exists for all &lt;math&gt;n \geq 2&lt;/math&gt;.</div></td></tr> </table> 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: «&#039;&#039;&#039;1-Factorization of &lt;math&gt;K_{2n}&lt;/math&gt;&#039;&#039;&#039; --- один-факторизация графа &lt;math&gt;K_{2n}&lt;/math&gt;. A &#039;&#039;&#039;one-factorization&#039;&#039;&#039; of &lt;math&gt;K_{2n}&lt;/math&gt;…»</p> <p><b>Новая страница</b></p><div>&#039;&#039;&#039;1-Factorization of &lt;math&gt;K_{2n}&lt;/math&gt;&#039;&#039;&#039; --- один-факторизация графа<br /> &lt;math&gt;K_{2n}&lt;/math&gt;. <br /> <br /> A &#039;&#039;&#039;one-factorization&#039;&#039;&#039; of &lt;math&gt;K_{2n}&lt;/math&gt; is a partition of the edge-set<br /> of &lt;math&gt;K_{2n}&lt;/math&gt; into &lt;math&gt;2n-1&lt;/math&gt; &#039;&#039;one-factors&#039;&#039;. A &#039;&#039;&#039;perfect one-factorization (P1F)&#039;&#039;&#039; is a one-factorization in which every pair of<br /> distinct one-factors forms a Hamiltonian cycle of &lt;math&gt;K_{2n}&lt;/math&gt;. P1Fs of<br /> &lt;math&gt;K_{2n}&lt;/math&gt; are known to exist when &lt;math&gt;2n-1&lt;/math&gt; or &lt;math&gt;n&lt;/math&gt; is prime, and for &lt;math&gt;2n<br /> \in \{16, 28, 36,40, 50, 126, 170, 244, 344, 730, \\ 1332, 1370, 1850,<br /> 2198, 3126, 6860, 12168, 16808, 29792\}&lt;/math&gt;.<br /> <br /> It has been conjectured that<br /> a perfect one-factorization of &lt;math&gt;K_{2n}&lt;/math&gt; exists for all &lt;math&gt;n \geq 2&lt;/math&gt;.</div> Glk