dc.contributor.author Sun, Hao dc.date.accessioned 2022-09-20 19:48:07 (GMT) dc.date.available 2022-09-20 19:48:07 (GMT) dc.date.issued 2022-09-20 dc.date.submitted 2022-09-08 dc.identifier.uri http://hdl.handle.net/10012/18764 dc.description.abstract Graph transversals are a classical branch of graph algorithms. In such a problem, one seeks a minimum-weight subset of nodes in a node-weighted graph $G$ which en intersects all copies of subgraphs~$F$ from a fixed family $\mathcal F$. In the first portion of this thesis we show two results related to even cycle transversal. %%Note rephrase this later. In Chapter \ref{ECTChapter}, we present our 47/7-approximation for even cycle transversal. To do this, we first apply a graph compression" method of Fiorini et al. % \cite{FioriniJP2010} which we describe in Chapter \ref{PreliminariesChapter}. For the analysis we repurpose the theory behind the 18/7-approximation for uncrossable" feedback vertex set problems of Berman and Yaroslavtsev %% \cite{BermanY2012} noting that we do not need the larger witness" cycles to be a cycle that we need to hit. This we do in Chapter \ref{BermanYaroChapter}. In Chapter \ref{ErdosPosaChapter} we present a simple proof of an Erdos Posa result, that for any natural number $k$ a planar graph $G$ either contains $k$ vertex disjoint even cycles, or a set $X$ of at most $9k$ such that $G \backslash X$ contains no even cycle. In the rest of this thesis, we show a result for dominating set. A dominating set $S$ in a graph is a set of vertices such that each node is in $S$ or adjacent to $S$. In Chapter 6 we present a primal-dual $(a+1)$-approximation for minimum weight dominating set in graphs of arboricity $a$. At the end, we propose five open problems for future research. dc.language.iso en en dc.publisher University of Waterloo en dc.subject even cycles en dc.subject planar graphs en dc.subject integrality gap en dc.subject bounded arboricity en dc.subject dominating set en dc.subject approximation algorithms en dc.subject graph transversal en dc.subject Erdős–Pósa en dc.title Transversal Problems In Sparse Graphs en dc.type Doctoral 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 Doctor of Philosophy en uws-etd.embargo.terms 0 en uws.contributor.advisor Koenemann, Jochen 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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