Abstract
A c-vertex-ranking of a graph G for a positive integer c is a labeling of the vertices of G with integers such that, for any label i, deletion of all vertices with labels > i leaves connected components, each having at most c vertices with label i. We present a polynomial-time algorithm to find a c-vertex-ranking of a partial k-tree using the minimum number of ranks for any bounded integers c and k.
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Kashem, M.A., Zhou, X., Nishizeki, T. (1997). Generalized vertex-rankings of partial k-trees. In: Jiang, T., Lee, D.T. (eds) Computing and Combinatorics. COCOON 1997. Lecture Notes in Computer Science, vol 1276. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0045088
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DOI: https://doi.org/10.1007/BFb0045088
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