Related papers: The Complexity of Clickomania

Motivated by a new way of visualizing hypergraphs, we study the following problem. Consider a rectangular grid and a set of colors $\chi$. Each cell $s$ in the grid is assigned a subset of colors $\chi_s \subseteq \chi$ and should be…

With increasing game size, a problem of computational complexity arises. This is especially true in real world problems such as in social systems, where there is a significant population of players involved in the game, and the complexity…

The Number Rotation Puzzle (NRP) is a combination puzzle in which the goal is to rearrange a scrambled rectangular grid of numbers back into order via moves that consist of rotating square blocks of numbers of fixed size. Over all possible…

Several articles deal with tilings with squares and dominoes on 2-dimensional boards, but only a few on boards in 3-dimensional space. We examine a tiling problem with colored cubes and bricks of $(2\times2\times n)$-board in three…

A c-coloring of G(n,m)=n x m is a mapping of G(n,m) into {1,...,c} such that no four corners forming a rectangle have the same color. In 2009 a challenge was proposed via the internet to find a 4-coloring of G(17,17). This attracted…

We consider the graph coloring game, a game in which two players take turns properly coloring the vertices of a graph, with one player attempting to complete a proper coloring, and the other player attempting to prevent a proper coloring.…

Here, we present a variant of the sliding coins game. Two coins are placed on distinct squares of a semi-infinite linear board with squares numbered $0, 1, 2, dots, $. Two players take turns and move a coin to a lower unoccupied square.…

We introduce a topological combinatorial game called the Link Smoothing Game. The game is played on the shadow of a link diagram and legal moves consist of smoothing precrossings. One player's goal is to keep the diagram connected while the…

In this paper, we consider a game played on a rectangular $m \times n$ gridded chocolate bar. Each move, a player breaks the bar along a grid line. Each move after that consists of taking any piece of chocolate and breaking it again along…

In this paper we study a single player game consisting of $n$ black checkers and $m$ white checkers, called shifting the checkers. We have proved that the minimum number of steps needed to play the game for general $n$ and $m$ is $nm + n +…

NP-complete problems should be hard on some instances but those may be extremely rare. On generic instances many such problems, especially related to random graphs, have been proven easy. We show the intractability of random instances of a…

We show that the following problems are NP-complete. 1. Can the vertex set of a graph be partitioned into two sets such that each set induces a perfect graph? 2. Is the difference between the chromatic number and clique number at most $1$…

A setup is proposed to play a quantum version of the famous bimatrix game of Prisoners' Dilemma. Multi-slit electron diffraction with each player's pure strategy consisting of opening one of the two slits at his/her disposal are essential…

A clique colouring of a graph is a colouring of the vertices such that no maximal clique is monochromatic (ignoring isolated vertices). The least number of colours in such a colouring is the clique chromatic number. Given $n$ points $x_1,…

We study the applicability of quantum algorithms in computational game theory and generalize some results related to Subtraction games, which are sometimes referred to as one-heap Nim games. In quantum game theory, a subset of Subtraction…

In cooperative games, the core is the most popular solution concept, and its properties are well known. In the classical setting of cooperative games, it is generally assumed that all coalitions can form, i.e., they are all feasible. In…

A random jigsaw puzzle is constructed by arranging $n^2$ square pieces into an $n \times n$ grid and assigning to each edge of a piece one of $q$ available colours uniformly at random, with the restriction that touching edges receive the…

Fibonacci nim is a popular impartial combinatorial game, usually played with a single pile of stones. The game is appealing due to its surprising connections with the Fibonacci numbers and the Zeckendorf representation. In this article, we…

A combinatorial game is a two-player game without hidden information or chance elements. One of the major approaches to analyzing games in combinatorial game theory is to break down a given game position into a disjunctive sum of multiple…

We study the Colored Bin Packing Problem: we are given a set of items where each item has a weight and color. We must pack the items in bins of uniform capacity such that no two items of the same color may be adjacent within in a bin. The…