Global Graph Properties byMeans of Local Computations : the Majority Problem
نویسندگان
چکیده
This paper is a contribution to the study of the general problem of characterizing those properties which can be computed on a graph or a network by means of local transformations. By using an abstract model based on graph relabelling systems we consider the majority problem : let G be a graph whose vertices have label A or B ; we say that label A has the majority if the number of A-labelled vertices is strictly greater than the number of B-labelled vertices (jGj A > jGj B). We prove that there exists graph relabelling systems deciding for every connected graph G whether jGj A > jGj B (resp. jGj A = jGj B) or not. On the other hand, we prove that no such system can decide if jGj A > jGj B ? m (resp. jGj A = jGj B ? m), for any positive integer m.
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