dc.contributor.author Murali, Karthik dc.date.accessioned 2022-07-18 14:11:54 (GMT) dc.date.available 2022-07-18 14:11:54 (GMT) dc.date.issued 2022-07-18 dc.date.submitted 2022-07-11 dc.identifier.uri http://hdl.handle.net/10012/18446 dc.description.abstract A separating set of a connected graph \$G\$ is a set of vertices \$S\$ such that \$G-S\$ is disconnected. \$S\$ is a minimum separating set of \$G\$ if there is no separating set of \$G\$ with fewer vertices than \$S\$. The size of a minimum separating set of \$G\$ is called the vertex connectivity of \$G\$. A separating set of \$G\$ that is a cycle is called a separating cycle of \$G\$. en Let \$G\$ be a planar graph with a given planar embedding. Let \$\Lambda(G)\$ be a supergraph of \$G\$ obtained by inserting a face vertex in each face of \$G\$ and connecting the face vertex to all vertices on the boundary of the face. It is well known that a set \$S\$ is a minimum separating set of a planar graph \$G\$ if and only if the vertices of \$S\$ can be connected together using face vertices to get a cycle \$X\$ of length \$2|S|\$ that is separating in \$\Lambda(G)\$. We extend this correspondence between separating sets and separating cycles from planar graphs to the class of bowtie 1-plane graphs. These are graphs that are embedded on the plane such that each edge is crossed at most once by another edge, and the endpoints of each such crossing induce either \$K_4\$, \$K_4 \setminus \{e\}\$ or \$C_4\$. Using this result, we give an algorithm to compute the vertex connectivity of a bowtie 1-plane graph in linear time. dc.language.iso en en dc.publisher University of Waterloo en dc.subject 1-planar graph en dc.subject vertex connectivity en dc.subject separating cycle en dc.title Testing vertex connectivity of bowtie 1-plane graphs en dc.type Master Thesis en dc.pending false uws-etd.degree.department David R. Cheriton School of Computer Science en uws-etd.degree.discipline Computer Science en uws-etd.degree.grantor University of Waterloo en uws-etd.degree Master of Mathematics en uws-etd.embargo.terms 0 en uws.contributor.advisor Biedl, Therese uws.contributor.affiliation1 Faculty of Mathematics en uws.published.city Waterloo en uws.published.country Canada en uws.published.province Ontario en uws.typeOfResource Text en uws.peerReviewStatus Unreviewed en uws.scholarLevel Graduate en
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