Cliques, size

Second, Kudo et al. (submitted) have shown that neocortex ratio correlates with with grooming clique size. This result suggests that species with larger neocortices can handle proportionately more relationships and keep them simultaneously functional. In this context, grooming cliques can be interpreted as alliances on which members rely in negotiat-... 

Kudo, H., Lowen, S. Dunbar, R. (submitted). Neocortex size as a constraint on grooming clique size in primates. Behaviour. 

Greater complexity where an individual s interactions with others are more common (e.g. higher rate of interaction, or more interactants) similarly, where more relationships are the rule (as in analyses based on clique size see Dunbar 1998). Further dyadic-level complexities include reciprocity (in grooming, for example) and exchange (where one type of benefit is traded for another). There is evidence for both these types of complexity in primates (Cords 1997). 

Use a clique-detection algorithm to identify the set of size-n cliques in G. 

Much of the same can be said about running tests to jueld lower bounds for the chromatic number. Even the most immediate one, computing the clique number, is not good, since this is an NP-complete problem as well. The existence of cliques of a fixed size can be decided in poljmomial time, but does not provide a very interesting test. 

Now, in order to find a optimal elimination order for this generic graph, we first recall that we are interested not only in finding the minimal number of fill-in edges to be added, but also that our goal is to limit the size of the maximum clique. Therefore, we observe the following properties about the first node to be removed from this graph ... 

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