Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Client-Waiter games on complete and random graphs   For a graph G, a monotone increasing graph property P and positive integer q,
we define the Client-Waiter game to be a two-player game which runs as follows.
In each turn Waiter is offering Client a subset of at least one and at most q+1
unclaimed edges of G from which Client claims one, and the rest are claimed by
Waiter. The game ends when all the edges have been claimed. If Client's graph
has property P by the end of the game, then he wins the game, otherwise Waiter
is the winner. In this paper we study several Client-Waiter games on the edge
set of the complete graph, and the H-game on the edge set of the random graph.
For the complete graph we consider games where Client tries to build a large
star, a long path and a large connected component. We obtain lower and upper
bounds on the critical bias for these games and compare them with the
corresponding Waiter-Client games and with the probabilistic intuition. For the
H-game on the random graph we show that the known results for the corresponding
Maker-Breaker game are essentially the same for the Client-Waiter game, and we
extend those results for the biased games and for trees.

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The categories of this paper are: stat
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The categories of this paper are: supr-con
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The categories of this paper are: ao-sci
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The categories of this paper are: eess
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-th
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The categories of this paper are: physics
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The categories of this paper are: q-fin
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The categories of this paper are: hep-th
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The categories of this paper are: cond-mat
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: adap-org
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The categories of this paper are: econ
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The categories of this paper are: solv-int