Introduced by Harris, Insko, Prieto Langarica, Stoisavljevic, and Sullivan, the tipsy cop and drunken robber is a variant of the cop and robber game on graphs in which the robber simply moves randomly along the graph, while the cop moves directed towards the robber some fixed proportion of the time and randomly the remainder. In this article, we adopt a slightly different interpretation of tipsiness of the cop and robber where we assume that in any round of the game there are four possible outcomes: a sober cop move, a sober robber move, a tipsy (uniformly random) move by the cop, and a tipsy (uniformly random) move by the robber. We study this tipsy cop and tipsy robber game on the infinite grid graph and on certain families of infinite trees including δ-regular trees and δ-regular trees rooted to a Δ-regular tree, where Δ≥δ. Our main results analyze strategies for the cop and robber on these graphs. We conclude with some directions for further study.

It is known that the cop number $c(G)$ of a connected graph $G$ can be bounded as a function of the genus of the graph $g(G)$. The best known bound, that $c(G) \leq \left\lfloor \frac{3 g(G)}{2}\right\rfloor + 3$, was given by Schröder, who conjectured that in fact $c(G) \leq g(G) + 3$. We give the first improvement to Schröder's bound, showing that $c(G) \leq \frac{4g(G)}{3} + \frac{10}{3}$.

Due to improvements in defensive systems, network threats are becoming increasingly sophisticated and complex as cybercriminals are using various methods to cloak their actions. This, among others, includes the application of network steganography e.g. to hide the communication between an infected host and a malicious control server by embedding commands into innocent-looking traffic. Currently, a new subtype of such methods called inter-protocol steganography emerged. It utilizes relationships between two or more overt protocols to hide data. In this paper, we present new inter-protocol hiding techniques which are suitable for real-time services. Afterwards, we introduce and present preliminary results of a novel steganography detection approach which relies on network traffic coloring.