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dc.contributor.authorHaddadan, Arash 20:09:07 (GMT) 20:09:07 (GMT)
dc.description.abstractWe study the following two problems: (1) finding a second room-partitioning of an oik, and (2) finding a second Hamiltonian cycle in cubic graphs. The existence of solution for both problems is guaranteed by a parity argument. For the first problem we prove that deciding whether a 2-oik has a room-partitioning is NP-hard, even if the 2-oik corresponds to a planar triangulation. For the problem of finding a second Hamiltonian cycle, we state the following conjecture: for every cubic planar bipartite graph finding a second Hamiltonian cycle can be found in time linear in the number of vertices via a standard pivoting algorithm. We fail to settle the conjecture, but we prove it for cubic planar bipartite WH(6)-minor free graphs.en
dc.publisherUniversity of Waterloo
dc.subjectParity argumenten
dc.subjectexchange algorithmen
dc.subjectcubic graphen
dc.subjectBarnette's conjectureen
dc.titleFinding a Second Hamiltonian cycle in Barnette Graphsen
dc.typeMaster Thesisen
dc.subject.programCombinatorics and Optimizationen and Optimizationen
uws-etd.degreeMaster of Mathematicsen

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