From social networks such as Facebook, the World Wide Web and the Internet, to the
complex interactions between proteins in the cells of our bodies, we constantly face the …

We study the problem of fairly allocating indivisible goods to groups of agents. Agents in the
same group share the same set of goods even though they may have different preferences …

An $ n $-vertex graph $ G $ is a $ C $-expander if $| N (X)|\geq C| X| $ for every $
X\subseteq V (G) $ with $| X|< n/2C $ and there is an edge between every two disjoint sets of …

Abstract We introduce the Maker–Breaker domination game, a two player game on a graph.
At his turn, the first player, Dominator, selects a vertex in order to dominate the graph while …

Abstract A graph G=(V, E) is called an expander if every vertex subset U of size up to| V|/2
has an external neighborhood whose size is comparable to| U|. Expanders have been a …

In a STOC 1976 paper, Schaefer proved that it is PSPACE-complete to determine the winner
of the so-called Maker-Breaker game on a given set system, even when every set has size at …

Abstract The Maker–Breaker total domination game in graphs is introduced as a natural
counterpart to the Maker–Breaker domination game recently studied by Duchêne, Gledel …

A typical result in graph theory says that a graph G, satisfying certain conditions, has some
property P. Once such a theorem is established, it is natural to ask how strongly G satisfies …

Long cycles in locally expanding graphs, with applications Page 1 COMBINATORICA Bolyai
Society – Springer-Verlag 0209–9683/119/$6.00 c 2019 János Bolyai Mathematical Society and …

Abstract The (m, n)-online Ramsey game is a combinatorial game between two players,
Builder and Painter. Starting from an infinite set of isolated vertices, Builder draws an edge …