Related papers: Creating spanning trees in Waiter-Client games

The graph grabbing game is played on a non-negatively weighted connected graph by Alice and Bob who alternately claim a non-cut vertex from the remaining graph, where Alice plays first, to maximize the weights on their respective claimed…

We propose a degree-preserving variant of the Builder--Chooser clique game of Pettie, Tardos, and Walczak. In each round, Builder chooses a matching, performs a degree-preserving growth (DPG) step by replacing the chosen edges with edges…

Consider a rooted Galton-Watson tree $T$, to each of whose edges we assign, independently, a weight that equals $+1$ with probability $p_{1}$, $0$ with probability $p_{0}$ and $-1$ with probability $p_{-1}=1-p_{1}-p_{0}$. We play a game on…

Let $n, k$ be positive integers. The $(k+1)$-star avoidance game on $K_n$ is played as follows. Two players take it in turn to claim a (previously unclaimed) edge of the complete graph on $n$ vertices. The first player to claim all edges of…

We prove that there exists a constant $c>0$ such that for all integers $2\leq t\leq cn$, if $\calA$ is a collection of spanning trees in $K_n$ such that any two intersect at at least $t$ edges, then $|\calA|\leq 2^tn^{n-t-2}$. This bound is…

We introduce a new type of positional games, played on a vertex set of a graph. Given a graph $G$, two players claim vertices of $G$, where the outcome of the game is determined by the subgraphs of $G$ induced by the vertices claimed by…

Let $L(G)$ denote the maximum number of leaves in any spanning tree of a connected graph $G$. We show the (known) result that for the $n$-cube $Q_n$, $L(Q_n) \sim 2^n = |V(Q_n)|$ as $n\rightarrow \infty$. Examining this more carefully,…

The network coloring game has been proposed in the literature of social sciences as a model for conflict-resolution circumstances. The players of the game are the vertices of a graph with $n$ vertices and maximum degree $\Delta$. The game…

We derive a sufficient condition for a sparse graph G on n vertices to contain a copy of a tree T of maximum degree at most d on (1-\epsilon)n vertices, in terms of the expansion properties of G. As a result we show that for fixed d\geq 2…

We introduce and study a Maker-Breaker type game in which the issue is to create or avoid two disjoint dominating sets in graphs without isolated vertices. We prove that the maker has a winning strategy on all connected graphs if the game…

We prove that in the biased 1:b Hamiltonicity Maker-Breaker game, played on the edges of the complete graph K_n, Maker has a winning strategy for b(n)<=(1-o(1))n/ln n, for all large enough n.

Maker-Breaker games are played on a hypergraph $(X,\mathcal{F})$, where $\mathcal{F} \subseteq 2^X$ denotes the family of winning sets. Both players alternately claim a predefined amount of edges (called bias) from the board $X$, and Maker…

We study the two-player game where Maker and Breaker alternately color the edges of a given graph $G$ with $k$ colors such that adjacent edges never get the same color. Maker's goal is to play such that at the end of the game, all edges are…

We study the $b$-biased Oriented-cycle game where two players, OMaker and OBreaker, take turns directing the edges of $K_n$ (the complete graph on $n$ vertices). In each round, OMaker directs one previously undirected edge followed by…

Motivated by the controller placement problems in software-defined networks and the fair division principles of classical "cake cutting", we investigate the following two-player zero-sum game. In our model, a defender places a limited…

The k-Tree algorithm [Wagner 02] is a non-trivial algorithm for the average-case k-SUM problem that has found widespread use in cryptanalysis. Its input consists of k lists, each containing n integers from a range of size m. Wagner's…

Consider a situation with $n$ agents or players where some of the players form a coalition with a certain collective objective. Simple games are used to model systems that can decide whether coalitions are successful (winning) or not…

We study the following combinatorial game played by two players, Alice and Bob, which generalizes the Pizza game considered by Brown, Winkler and others. Given a connected graph G with nonnegative weights assigned to its vertices, the…

In the concurrent graph sharing game, two players, called First and Second, share the vertices of a connected graph with positive vertex-weights summing up to $1$ as follows. The game begins with First taking any vertex. In each proceeding…

In this paper, we continue the study of the total domination game in graphs introduced in [Graphs Combin. 31(5) (2015), 1453--1462], where the players Dominator and Staller alternately select vertices of $G$. Each vertex chosen must…