Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Weak and Strong k-connectivity games   For a positive integer $k$ we consider the $k$-vertex-connectivity game,
played on the edge set of $K_n$, the complete graph on $n$ vertices. We first
study the Maker-Breaker version of this game and prove that, for any integer $k
\geq 2$ and sufficiently large $n$, Maker has a strategy for winning this game
within $\lfloor k n/2 \rfloor + 1$ moves, which is clearly best possible. This
answers a question of Hefetz, Krivelevich, Stojakovi\'c and Szab\'o. We then
consider the strong $k$-vertex-connectivity game. For every positive integer
$k$ and sufficiently large $n$, we describe an explicit first player's winning
strategy for this game.

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The categories of this paper are: plasm-ph
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The categories of this paper are: nlin
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The categories of this paper are: atom-ph
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The categories of this paper are: math-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: solv-int
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The categories of this paper are: q-alg
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The categories of this paper are: comp-gas
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The categories of this paper are: econ
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The categories of this paper are: chao-dyn
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The categories of this paper are: acc-phys
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The categories of this paper are: chem-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-th