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dc.contributor.authorSun, Hao 19:48:07 (GMT) 19:48:07 (GMT)
dc.description.abstractGraph 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 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.en
dc.publisherUniversity of Waterlooen
dc.subjecteven cyclesen
dc.subjectplanar graphsen
dc.subjectintegrality gapen
dc.subjectbounded arboricityen
dc.subjectdominating seten
dc.subjectapproximation algorithmsen
dc.subjectgraph transversalen
dc.titleTransversal Problems In Sparse Graphsen
dc.typeDoctoral Thesisen
dc.pendingfalse and Optimizationen and Optimizationen of Waterlooen
uws-etd.degreeDoctor of Philosophyen
uws.contributor.advisorKoenemann, Jochen
uws.contributor.affiliation1Faculty of Mathematicsen

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