# Vol. 18 no. 1

### 1. Persisting randomness in randomly growing discrete structures: graphs and search trees

The successive discrete structures generated by a sequential algorithm from random input constitute a Markov chain that may exhibit long term dependence on its first few input values. Using examples from random graph theory and search algorithms we show how such persistence of randomness can be […]
Section: Analysis of Algorithms

### 2. The game colouring number of powers of forests

We prove that the game colouring number of the $m$-th power of a forest of maximum degree $\Delta\ge3$ is bounded from above by $\frac{(\Delta-1)^m-1}{\Delta-2}+2^m+1,$ which improves the best known bound by an asymptotic factor of 2.
Section: Graph Theory