相关论文: Drawing strategies in Strong Ramsey games for 3-un…

Consider a game played on the edge set of the infinite clique by two players, Builder and Painter. In each round, Builder chooses an edge and Painter colours it red or blue. Builder wins by creating either a red copy of $G$ or a blue copy…

For an integer $k \geq 2$, an ordered $k$-uniform hypergraph $\mathcal{H}=(H,<)$ is a $k$-uniform hypergraph $H$ together with a fixed linear ordering $<$ of its vertex set. The ordered Ramsey number $\overline{R}(\mathcal{H},\mathcal{G})$…

The $[X,Y]$-edge colouring game is played with a set of $k$ colours on a graph $G$ with initially uncoloured edges by two players, Alice (A) and Bob (B). The players move alternately. Player $X\in\{A,B\}$ has the first move.…

The classical result in the theory of random graphs, proved by Erdos and Renyi in 1960, concerns the threshold for the appearance of the giant component in the random graph process. We consider a variant of this problem, with a Ramsey…

In 1982, Harary introduced the concept of Ramsey achievement game on graphs. Given a graph $F$ with no isolated vertices. Consider the following game played on the complete graph $K_n$ by two players Alice and Bob. First, Alice colors one…

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…

We study Ramsey properties of randomly perturbed $3$-uniform hypergraphs. For~$t\geq 2$, write $\tilde K^{(3)}_t$ to denote the $3$-uniform {\it expanded} clique hypergraph obtained from the complete graph $K_t$ by expanding each of the…

The semi-random graph process is a single-player game that begins with an empty graph on $n$ vertices. In each round, a vertex $u$ is presented to the player independently and uniformly at random. The player then adaptively selects a vertex…

Given a $k$-uniform hypergraph $G$ and a set of $k$-uniform hypergraphs $\mathcal{H}$, the generalized Ramsey number $f(G,\mathcal{H},q)$ is the minimum number of colors needed to edge-color $G$ so that every copy of every hypergraph $H\in…

We show that quantum graph parameters for finite, simple, undirected graphs encode winning strategies for all possible synchronous non-local games. Given a synchronous game $\mathcal{G}=(I,O,\lambda)$ with $|I|=n$ and $|O|=k$, we…

For graphs $G$ and $H$, let $G\to H$ signify that any red/blue edge coloring of $G$ contains a monochromatic $H$. Let $G(N,p)$ be the random graph of order $N$ and edge probability $p$. The Ramsey thresholds for fixed graphs have received…

Given two graphs $G$ and $H$, the online Ramsey number $\tilde{r}(G,H)$ is defined to be the minimum number of rounds that Builder can always guarantee a win in the following $(G, H)$-online Ramsey game between Builder and Painter. Starting…

We investigate Ramsey properties of a random graph model in which random edges are added to a given dense graph. Specifically, we determine lower and upper bounds on the function $p=p(n)$ that ensures that for any dense graph $G_n$ a.a.s.…

For a fixed set of positive integers $R$, we say $\mathcal{H}$ is an $R$-uniform hypergraph, or $R$-graph, if the cardinality of each edge belongs to $R$. An $R$-graph $\mathcal{H}$ is \emph{covering} if every vertex pair of $\mathcal{H}$…

An online Ramsey game is a game between Builder and Painter, alternating in turns. They are given a graph $H$ and a graph $G$ of an infinite set of independent vertices. In each round Builder draws an edge and Painter colors it either red…

Given a hypergraph $H$, the size-Ramsey number $\hat{r}_2(H)$ is the smallest integer $m$ such that there exists a graph $G$ with $m$ edges with the property that in any colouring of the edges of $G$ with two colours there is a…

Given a graph G and an integer k, two players take turns coloring the vertices of G one by one using k colors so that neighboring vertices get different colors. The first player wins iff at the end of the game all the vertices of $G$ are…

In this note we consider a Ramsey property of random $d$-regular graphs, $\mathcal{G}(n,d)$. Let $r\ge 2$ be fixed. Then w.h.p. the edges of $\mathcal{G}(n, 2r)$ can be colored such that every monochromatic component has size $o(n)$. On the…

A $d$-defective $k$-painting game on a graph $G$ is played by two players: Lister and Painter. Initially, each vertex is uncolored and has $k$ tokens. In each round, Lister marks a chosen set $M$ of uncolored vertices and removes one token…

Motivated by the success of domination games and by a variation of the coloring game called the indicated coloring game, we introduce a version of domination games called the indicated domination game. It is played on an arbitrary graph $G$…