Balanced Avoidance Games on Random Graphs

Online balanced graph avoidance games

We introduce and study online balanced coloring games on the random graph process. The game is played by a player we call Painter. Edges of the complete graph with n vertices are introduced two at the time, in a random order. For each pair of edges, Painter immediately and irrevocably chooses one of the two possibilities to color one of them red and the other one blue. His goal is to avoid crea...

Balanced Online Edge Coloring Games on Random Graphs

Offline thresholds for Ramsey-type games on random graphs

In this paper, we compare the offline versions of three Ramsey-type oneplayer games that have been studied in an online setting in previous work: the online Ramsey game, the balanced online Ramsey game, and the Achlioptas game. The goal in all games is to color the edges of the random graph Gn,m according to certain rules without creating a monochromatic copy of some fixed forbidden graph H. Wh...

On some approximately balanced combinatorial cooperative games

A model of taxation for cooperative n-person games is introduced where proper coalitions are taxed proportionally to their value. Games with non-empty core under taxation at rate e are a-balanced. Sharp bounds on e in matching games on (not necessarily bipartite) graphs are established. Upper and lower bounds on the smallest e in bin packing games are derived and euclidean random TSP games are ...

On Balanced Coloring Games in Random Graphs

Consider the balanced Ramsey game, in which a player has r colors and where in each round r random edges of an initially empty graph on n vertices are presented. The player has to immediately assign a different color to each edge and her goal is to avoid creating a monochromatic copy of some fixed graph F for as long as possible. The Achlioptas game is similar, but the player only loses when sh...