Search Game on the Union of N Identical Graphs Joined at One or Two Points

Ljiljana Pavlović

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A graph-theoretic characterization of the core in a homogeneous generalized assignment game

Tadeusz Sozański (2006)

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An exchange network is a socioeconomic system in which any two actors are allowed to negotiate and conclude a transaction if and only if their positions-mathematically represented by the points of a connected graph-are joined by a line of this graph. A transaction consists in a bilaterally agreed-on division of a profit pool assigned to a given line. Under the one-exchange rule, every actor is permitted to make no more than one transaction in each negotiation round. Bienenstock and Bonacich...

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Cvetković, Dragoš, Pevac, Irena (1984)

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A tandem version of the cops and robber game played on products of graphs

Nancy E. Clarke, Richard J. Nowakowski (2005)

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In this version of the Cops and Robber game, the cops move in tandems, or pairs, such that they are at distance at most one from each other after every move. The problem is to determine, for a given graph G, the minimum number of tandems sufficient to guarantee a win for the cops. We investigate this game on three graph products, the Cartesian, categorical and strong products.

Note: The Smallest Nonevasive Graph Property

Michał Adamaszek (2014)

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A property of n-vertex graphs is called evasive if every algorithm testing this property by asking questions of the form “is there an edge between vertices u and v” requires, in the worst case, to ask about all pairs of vertices. Most “natural” graph properties are either evasive or conjectured to be such, and of the few examples of nontrivial nonevasive properties scattered in the literature the smallest one has n = 6. We exhibit a nontrivial, nonevasive property of 5-vertex graphs...

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Nešetřil, J., Sopena, E. (2001)

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Information flows, graphs and their guessing numbers.

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Note On The Game Colouring Number Of Powers Of Graphs

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We generalize the methods of Esperet and Zhu [6] providing an upper bound for the game colouring number of squares of graphs to obtain upper bounds for the game colouring number of m-th powers of graphs, m ≥ 3, which rely on the maximum degree and the game colouring number of the underlying graph. Furthermore, we improve these bounds in case the underlying graph is a forest.

On winning fast in Avoider-Enforcer games.

Barát, János, Stojaković, Miloš (2010)

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K. Howalla, Abdallah N. Dabboucy, R. Tout (1983)

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Game colouring directed graphs.

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Search Game on an Odd Number of Arcs with Immobile Hider

Ljiljana Pavlović (1993)

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