<?xml version="1.0" encoding="UTF-8"?> <article key="pdf/10536" mdate="2009-09-28 00:00:00"> <author>Sizhong Zhou</author> <title>A Sufficient Condition for Graphs to Have Hamiltonian a, bFactors</title> <pages>704 - 706</pages> <year>2009</year> <volume>3</volume> <number>9</number> <journal>International Journal of Mathematical and Computational Sciences</journal> <ee>https://publications.waset.org/pdf/10536</ee> <url>https://publications.waset.org/vol/33</url> <publisher>World Academy of Science, Engineering and Technology</publisher> <abstract>Let a and b be nonnegative integers with 2 &amp;amp;le; a &amp;amp;lt; b, and let G be a Hamiltonian graph of order n with n &amp;amp;ge; (ab&amp;amp;minus;4)(ab&amp;amp;minus;2) b&amp;amp;minus;2 . An a, bfactor F of G is called a Hamiltonian a, bfactor if F contains a Hamiltonian cycle. In this paper, it is proved that G has a Hamiltonian a, bfactor if NG(X) &amp;amp;gt; (a&amp;amp;minus;1)nX&amp;amp;minus;1 ab&amp;amp;minus;3 for every nonempty independent subset X of V (G) and &amp;amp;delta;(G) &amp;amp;gt; (a&amp;amp;minus;1)nab&amp;amp;minus;4 ab&amp;amp;minus;3 . </abstract> <index>Open Science Index 33, 2009</index> </article>