dc.contributor.author Ibrahimpur, Sharat dc.date.accessioned 2016-09-27 22:02:26 (GMT) dc.date.available 2016-09-27 22:02:26 (GMT) dc.date.issued 2016-09-27 dc.date.submitted 2016-09-26 dc.identifier.uri http://hdl.handle.net/10012/10939 dc.description.abstract In this thesis, we investigate the problem of packing and covering odd $(u,v)$-trails in a graph. A $(u,v)$-trail is a $(u,v)$-walk that is allowed to have repeated vertices but no repeated edges. We call a trail \emph{odd} if the number of edges in the trail is odd. Given a graph $G$ and two specified vertices $u$ and $v$, the odd $(u,v)$-trail packing number, denoted by $\nu(u,v)$, is the maximum number of edge-disjoint odd $(u,v)$-trails in $G$. And, the odd $(u,v)$-trail covering number, denoted by $\tau(u,v)$, is the minimum size of an edge-set that intersects every odd $(u,v)$-trail in $G$. In 2016, Churchley, Mohar, and Wu, were the first ones to prove a constant factor bound on the \coverpack ratio, by showing that $\tau(u,v) \leq 8 \cdot \nu(u,v)$. Our main result in this thesis is an improved bound on the covering number: $\tau(u,v) \leq 5 \cdot \nu(u,v) + 2$. The proof leads to a polynomial-time algorithm to find, for any given $k \geq 1$, either $k$ edge-disjoint odd $(u,v)$-trails in $G$ or a set of at most $5k-3$ edges intersecting all odd $(u,v)$-trails in $G$. en dc.language.iso en en dc.publisher University of Waterloo en dc.title Packing and Covering Odd (u,v)-trails in a Graph en dc.type Master Thesis en dc.pending false uws-etd.degree.department Combinatorics and Optimization en uws-etd.degree.discipline Combinatorics and Optimization en uws-etd.degree.grantor University of Waterloo en uws-etd.degree Master of Mathematics en uws.contributor.advisor Swamy, Chaitanya 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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