Damanik, David2009-06-032009-06-032008Jennings, Landon. "New sufficient condition for Hamiltonian paths." (2008) Diss., Rice University. <a href="https://hdl.handle.net/1911/22232">https://hdl.handle.net/1911/22232</a>.https://hdl.handle.net/1911/22232This paper proves a sufficient condition for the existence of Hamiltonian paths in simple connected graphs. This condition was conjectured in 2006 by a computer program named Graffiti.pc. Given examples will show that this new condition detects Hamiltonian paths that a theorem by Chvatal does not. A second condition conjectured by Graffiti.pc is shown to satisfy Chvatal's condition. Thus this second conjecture, while true, does not improve on known results.39 p.application/pdfengCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.MathematicsThesisTHESIS MATH. 2008 JENNINGS