Related papers: Weighted tree games

Maker-Breaker total domination game in graphs is introduced as a natural counterpart to the Maker-Breaker domination game recently studied by Duch\^ene, Gledel, Parreau, and Renault. Both games are instances of the combinatorial…

One of the main objective of this paper is to relate Beck's conjecture for k-in-a-row games. The conjecture states that playing on the same board Picker is better off in a Chooser-Picker game than the second player in the Maker-Breaker…

With the advance of complex large-scale networks, it is becoming increasingly important to understand how selfish and spatially distributed individuals will share network resources without centralized coordinations. In this paper, we…

The notions of captured/lost vertices and dead edges in the Shannon game (Shannon switching game on nodes) are examined using graph theory. Simple methods are presented for identifying some dead edges and some captured sets of vertices,…

We study (a:a) Maker-Breaker games played on the edge set of the complete graph on n vertices. In the following four games - perfect matching game, Hamilton cycle game, star factor game and path factor game, our goal is to determine the…

Every weighted tree corresponds naturally to a cooperative game that we call a "tree game"; it assigns to each subset of leaves the sum of the weights of the minimal subtree spanned by those leaves. In the context of phylogenetic trees, the…

We study a controlled random graph process introduced by Frieze, Krivelevich, and Michaeli. In this model, the edges of a complete graph are randomly ordered and revealed sequentially to a builder. For each edge revealed, the builder must…

Random graphs are more and more used for modeling real world networks such as evolutionary networks of proteins. For this purpose we look at two different models and analyze how properties like connectedness and degree distributions are…

We derive two formulas for the weighted sums of rooted spanning forests of particular sequence of graphs by using the matrix tree theorem. We consider cycle graphs with edges so called the pendant edges. One of our formula can be described…

It is required to find an optimal order of constructing the edges of a network so as to minimize the sum of the weighted connection times of relevant pairs of vertices. Construction can be performed anytime anywhere in the network, with a…

Weighted timed games are two-player zero-sum games played in a timed automaton equipped with integer weights. We consider optimal reachability objectives, in which one of the players, that we call Min, wants to reach a target location while…

In a strong game played on the edge set of a graph G there are two players, Red and Blue, alternating turns in claiming previously unclaimed edges of G (with Red playing first). The winner is the first one to claim all the edges of some…

In the Maker-Breaker vertex colouring game, first publicised by Gardner in 1981, Maker and Breaker alternately colour vertices of a graph using a fixed palette, maintaining a proper colouring at all times. Maker aims to colour the whole…

We present new approaches to constructing graph sparsifiers --- weighted subgraphs for which every cut has the same value as the original graph, up to a factor of $(1 \pm \epsilon)$. Our first approach independently samples each edge $uv$…

We propose a random bipartite graph with weights assigned to both parts of the vertex sets. Edges are formed independently with probabilities that depend on these weights. This bipartite graph naturally gives rise to a random intersection…

Wagering mechanisms are one-shot betting mechanisms that elicit agents' predictions of an event. For deterministic wagering mechanisms, an existing impossibility result has shown incompatibility of some desirable theoretical properties. In…

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…

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 $k \geq 2$…

We introduce the concept of budget games. Players choose a set of tasks and each task has a certain demand on every resource in the game. Each resource has a budget. If the budget is not enough to satisfy the sum of all demands, it has to…

The main result of this paper is that computing the value of a one-clock priced timed game (OCPTG) is PSPACE-hard. Along the way, we provide a family of OCPTGs that have an exponential number of event points. Both results hold even in very…