Long cycles in locally expanding graphs, with applications Page 1 COMBINATORICA Bolyai
Society – Springer-Verlag 0209–9683/119/$6.00 c 2019 János Bolyai Mathematical Society and …

We show that every locally sparse graph contains a linearly sized expanding subgraph. For
constants c_1> c_2> 1, 0< α< 1, a graph G on n vertices is called a (\c_1, c_2, α)-graph if it …

We study two types of two player, perfect information games with no chance moves, played
on the edge set of the binomial random graph G (n, p). In each round of the (1: q) Waiter …

Waiter-Client games are played on some hypergraph $(X,\mathcal {F}) $, where $\mathcal
{F} $ denotes the family of winning sets. For some bias $ b $, during each round of such a …

For a graph G, a monotone increasing graph property P and positive integer q, we define the
Client-Waiter game to be a two-player game which runs as follows. In each turn Waiter is …

Fix two integers n, k, with n divisible by k, and consider the following game played by two
players, Waiter and Client, on the edges of K n. Starting with all the edges marked as …

The topic of this thesis are different variants of Maker-Breaker positional game, where two
players Maker and Breaker alternatively take turns in claiming unclaimed edges/vertices of a …

We study the positional game where two players, Maker and Breaker, alternately select
respectively 1 and b previously unclaimed edges of K n. Maker wins if she succeeds in …

In this paper we consider positional games where the winning sets are tree universal
graphs. Specifically, we show that in the unbiased Maker-Breaker game on the complete …

For integers $ n, D, q $ we define a two player perfect information game with no chance
moves called the Waiter-Client Maximum Degree game. In this game, two players (Waiter …