منابع مشابه
Internal Partitions of Regular Graphs
An internal partition of an n-vertex graph G = (V,E ) is a partition of V such that every vertex has at least as many neighbors in its own part as in the other part. It has been conjectured that every d -regular graph with n > N(d ) vertices has an internal partition. Here we prove this for d = 6. The case d = n − 4 is of particular interest and leads to interesting new open problems on cubic g...
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In this paper an efficient method is developed for the analysis of non-regular graphs which contain regular submodels. A model is called regular if it can be expressed as the product of two or three subgraphs. Efficient decomposition methods are available in the literature for the analysis of some classes of regular models. In the present method, for a non-regular model, first the nodes of the ...
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A complete partition of a graph is a partition of the vertex set such that any two classes are connected by an edge. We consider the problem of finding a complete partition maximizing the number of classes. This relates to clustering into the greatest number of groups so as to minimize the diameter (inter-cluster connectivity) without concern for the intra-cluster topology. We give a randomized...
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We try to develop a theory of ω-regular partitions in parallel with the theory around the Wagner hierarchy of regular ω-languages. In particular, we generalize a theorem of L. Staiger and K. Wagner to the case of partitions, prove decidability of all levels of the Boolean hierarchy of regular partitions over open sets, establish coincidence of reducibilities by continuous functions and by funct...
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ژورنال
عنوان ژورنال: Canadian Mathematical Bulletin
سال: 1978
ISSN: 0008-4395,1496-4287
DOI: 10.4153/cmb-1978-030-4