INDUCTIVE COMPUTATIONS ON GRAPHS DEFINEDBY CLIQUE-WIDTH EXPRESSIONS

Labelling problems for graphs consist in buildingdistributed data structures, making it possible to check a given graphproperty or to compute a given function, the arguments of which arevertices. For an inductively computable function D, if G is a graphwith n vertices and of clique-width at most k, where k is fixed, we canassociate with each vertex x of G a piece of information (bit sequence)lab(x) of length O(log2(n)) such that we can compute D in constanttime, using only the labels of its arguments. The preprocessing can bedone in time O(h.n) where h is the height of the syntactic tree of G. Weperform an inductive computation, without using the tools of monadicsecond order logic. This enables us to give an explicit labelling schemeand to avoid constants of exponential size