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    Acyclic 5-Choosability of Planar Graphs Without Adjacent Short Cycles

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    Thesis (626.5Kb)
    Date
    2013-09-05
    Author
    Ferreri, Susanna
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    Abstract
    The conjecture claiming that every planar graph is acyclic 5-choosable[Borodin et al., 2002] has been verified for several restricted classes of planargraphs. Recently, O. V. Borodin and A. O. Ivanova, [Journal of Graph Theory,68(2), October 2011, 169-176], have shown that a planar graph is acyclically 5-choosable if it does not contain an i-cycle adjacent to a j-cycle, where 3<=j<=5 if i=3 and 4<=j<=6 if i=4. We improve the above mentioned result and prove that every planar graph without an i-cycle adjacent to a j-cycle with3<=j<=5 if i=3 and 4<=j<=5 if i=4 is acyclically 5-choosable.
    URI
    http://hdl.handle.net/10464/4957
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