Related papers: Mis\`ere-play Hackenbush Sprigs

We consider deformations of D-brane systems induced by a change in the closed string background in the framework of bosonic open-closed string field theory, where it is possible to unambiguously tame infrared divergences originating from…

The present paper deals with connected subtraction games in graphs, which are generalization of takeaway games. In a connected subtraction game, two players alternate removing a connected sub-graph from a given connected game-graph,…

It is well known that if the nonempty player of the Banach-Mazur game has a winning strategy on a space, then that space is Baire in all powers even in the box topology. The converse of this implication may be true also: We know of no…

A move in the game of nim consists of taking any positive number of tokens from a single pile. Suppose we add the class of moves of taking a nonnegative number of tokens jointly from all the piles. We give a complete answer to the question…

An algebraic linear ordering is a component of the initial solution of a first-order recursion scheme over the continuous categorical algebra of countable linear orderings equipped with the sum operation and the constant 1. Due to a general…

We classify the periodic digit strings which arise from periodic billiard orbits on the four convex $n$-gons $\Delta$ which tile $\mathbb{R}^2$ under reflection, answering problem a posed by Baxter and Umble. $\Delta$ is either an…

State-of-the-art methods for solving 2-player zero-sum imperfect information games rely on linear programming or regret minimization, though not on dynamic programming (DP) or heuristic search (HS), while the latter are often at the core of…

I present a formal connection between algebraic effects and game semantics, two important lines of work in programming languages semantics with applications in compositional software verification. Specifically, the algebraic signature…

In this article, we define the notion of slim (normal) bases and show their existence for various fields. As an application, an algorithm will be given that computes the spectrum of a basefield transform by merely using O(n) additions.

Hex is a well known connection game in which two players attempt to connect opposite sides of the board by colored stones. In 2022, Hamkins and Leonessi introduced an infinite version, in which the goal is to construct a certain kind of…

A graph $G$ is said to be perfectly divisible if for every induced subgraph $H$ of $G$ with at least one edge, the vertex set $V(H)$ can be partitioned into two sets $A, B$ such that $H[A]$ is perfect and $\omega(B) < \omega(H)$. It is easy…

We consider a class of deterministic mean field games, where the state associated with each player evolves according to an ODE which is linear w.r.t. the control. Existence, uniqueness, and stability of solutions are studied from the point…

By resorting to the vector space structure of finite games, skew-symmetric games (SSGs) are proposed and investigated as a natural subspace of finite games. First of all, for two player games, it is shown that the skew-symmetric games form…

Given a graph $G=(V,E)$ on $n$ vertices and an assignment of colours to its edges, a set of edges $S \subseteq E$ is said to be rainbow if edges from $S$ have pairwise different colours assigned to them. In this paper, we investigate…

A proper edge $t$-coloring of a graph $G$ is a coloring of edges of $G$ with colors $1,2,...,t$ such that all colors are used, and no two adjacent edges receive the same color. The set of colors of edges incident with a vertex $x$ is called…

Consider a vertex colouring game played on a simple graph with $k$ permissible colours. Two players, a maker and a breaker, take turns to colour an uncoloured vertex such that adjacent vertices receive different colours. The game ends once…

Frank Harary introduced the concept of integral sum graph. A graph $G$ is an \emph{ integral sum graph} if its vertices can be labeled with distinct integers so that $e = uv$ is an edge of $G$ if and only if the sum of the labels on…

Sprouts is a two-player topological game, invented in 1967 by Michael Paterson and John Conway. The game starts with p spots drawn on a sheet of paper, and lasts at most 3p-1 moves: the player who makes the last move wins. Sprouts is a very…

When $H$ is a forest, the Gy\'arf\'as-Sumner conjecture implies that every graph $G$ with no induced subgraph isomorphic to $H$ and with bounded clique number has a stable set of linear size. We cannot prove that, but we prove that every…

If $\mathfrak{g}$ is a Frobenius Lie algebra, then for certain $F\in \mathfrak{g}^*$ the natural map $\mathfrak{g}\longrightarrow \mathfrak{g}^* $ given by $x \longmapsto F[x,-]$ is an isomorphism. The inverse image of $F$ under this…