It is well known that individuals can route messages on short paths through
social networks, given only simple information about the target and using only
local knowledge about the topology. Sociologists conjecture that people find
routes greedily by passing the message to an acquaintance that has more in
common with the target than themselves, e.g. if a dentist in Saarbr\"ucken
wants to send a message to a specific lawyer in Munich, he may forward it to
someone who is a lawyer and/or lives in Munich. Modelling this setting,
Eppstein et al. introduced the notion of category-based routing. The goal is to
assign a set of categories to each node of a graph such that greedy routing is
possible. By proving bounds on the number of categories a node has to be in we
can argue about the plausibility of the underlying sociological model. In this
paper we substantially improve the upper bounds introduced by Eppstein et al.
and prove new lower bounds.Comment: 21 page
