3 research outputs found

    Embedding a Forest in a Graph

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    For \math{p\ge 1}, we prove that every forest with \math{p} trees whose sizes are a1,...,apa_1,..., a_p can be embedded in any graph containing at least ∑i=1p(ai+1)\sum_{i=1}^p (a_i + 1) vertices and having a minimum degree at least ∑i=1pai\sum_{i=1}^p a_i.Comment: Working paper, submitte

    On the Turan number of forests

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    The Turan number of a graph H, ex(n,H), is the maximum number of edges in a graph on n vertices which does not have H as a subgraph. We determine the Turan number and find the unique extremal graph for forests consisting of paths when n is sufficiently large. This generalizes a result of Bushaw and Kettle [ Combinatorics, Probability and Computing 20:837--853, 2011]. We also determine the Turan number and extremal graphs for forests consisting of stars of arbitrary order
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