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dc.contributor.authorRedlin, Shayla 20:29:17 (GMT) 20:29:17 (GMT)
dc.description.abstractAn acyclic k-colouring of a graph G is a proper k-colouring of G with no bichromatic cycles. In 1979, Borodin proved that planar graphs are acyclically 5-colourable, an analog of the Four Colour Theorem. Kawarabayashi and Mohar proved in 2010 that "locally" planar graphs are acyclically 7-colourable, an analog of Thomassen's result that "locally" planar graphs are 5-colourable. We say that a graph G is critical for (acyclic) k-colouring if G is not (acyclically) k-colourable, but all proper subgraphs of G are. In 1997, Thomassen proved that for every k >= 5 and every surface S, there are only finitely many graphs that embed in S that are critical for k-colouring. Here we prove the analogous result that for each k >= 12 and each surface S, there are finitely many graphs embeddable on S that are critical for acyclic k-colouring. This result implies that there exists a linear time algorithm that, given a surface S and large enough k, decides whether a graph embedded in S is acyclically k-colourable.en
dc.publisherUniversity of Waterlooen
dc.subjectgraph theoryen
dc.subjectgraph colouringen
dc.subjectacyclic colouringen
dc.subjectcolouring graphs on surfacesen
dc.subjectcritical graphsen
dc.titleAcyclic Colouring of Graphs on Surfacesen
dc.typeMaster Thesisen
dc.pendingfalse and Optimizationen and Optimizationen of Waterlooen
uws-etd.degreeMaster of Mathematicsen
uws.contributor.advisorPostle, Luke
uws.contributor.affiliation1Faculty of Mathematicsen

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