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A comprehensive analysis of degree based condition for Hamiltonian cycles
Hasan, Md. Kamrul,Kaykobad, Mohammad,Lee, Young-Koo,Lee, Sungyoung Elsevier 2010 Theoretical computer science Vol.411 No.1
<P><B>Abstract</B></P><P>Since finding whether a graph has a Hamiltonian path or Hamiltonian cycle are both NP-complete problems, researchers have been formulating sufficient conditions that ensure the path or cycle. Rahman and Kaykobad (2005) <ce:cross-ref refid='b2'>[2]</ce:cross-ref> presented a sufficient condition for determining the existence of Hamiltonian path. Three recent works–Lenin Mehedy, Md. Kamrul Hasan, Mohammad Kaykobad (2007) <ce:cross-ref refid='b3'>[3]</ce:cross-ref>, Rao Li (2006) <ce:cross-ref refid='b4'>[4]</ce:cross-ref>, Shengjia Li, Ruijuan Li, Jinfeng Feng (2007) <ce:cross-ref refid='b5'>[5]</ce:cross-ref>–further used the same or similar condition to ensure Hamiltonian cycle with some exceptions. The three works, along with their unique findings, have some common results. This paper unifies the results and brings them under Rahman and Kaykobad’s condition.</P>