31 research outputs found

    Orchestrating Mathematical Classroom Discourse About Various Solution Methods: Case Study of a Teacher’s Development

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    Contains fulltext : 216038pub.pdf (publisher's version ) (Open Access

    Building on student mathematical thinking in whole-class discourse: exploring teachers' in-the-moment decision-making, interpretation, and underlying conceptions

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    Contains fulltext : 242931.pdf (Publisher’s version ) (Open Access)28 mei 202125 p

    Large Independent Sets in Triangle-Free Planar Graphs

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    Every triangle-free planar graph on n vertices has an independent set of size at least (n+1)/3, and this lower bound is tight. We give an algorithm that, given a triangle-free planar graph G on n vertices and an integer k>=0, decides whether G has an independent set of size at least (n+k)/3, in time 2^{O(sqrt{k})}n. Thus, the problem is fixed-parameter tractable when parameterized by k. Furthermore, as a corollary of the result used to prove the correctness of the algorithm, we show that there exists epsilon>0 such that every planar graph of girth at least five on n vertices has an independent set of size at least n/(3-epsilon).Comment: 14 pages, 1 figur
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