In this article, we analyze the appearance of a Hamilton cycle in the following random
process. The process starts with an empty graph on nlabeled vertices. At each round we are …

The standard paradigm for online power of two choices problems in random graphs is the
Achlioptas process. Here we consider the following natural generalization: Starting with G0 …

Consider the following one-player game. Starting with the empty graph on $ n $ vertices, in
every step $ r $ new edges are drawn uniformly at random and inserted into the current …

In this article, we compare the offline versions of three Ramsey‐type one‐player games that
have been studied in an online setting in previous work: the online Ramsey game, the …

We study the problem of creating a copy of some fixed graph H in the Achlioptas process on
n vertices with parameter r, where r=r(n) is a growing function of n. We prove general upper …

The basic premise of Ramsey Theory states that in a sufficiently large system, complete
disorder is impossible. One instance from the world of graph theory says that given two fixed …

In this thesis we deal with games in the intersection of extremal combinatorics and random
graph theory which gained a lot of attention over the past decades. Consider the following …

We consider variants of the triangle-avoidance game first defined by Harary and
rediscovered by Hajnal a few years later. A graph game begins with two players and an …

Consider the balanced Ramsey game, in which a player has r colors and where in each step
r random edges of an initially empty graph on n vertices are presented. The player has to …

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 …