Generalized vertex-rankings of trees

Xiao Zhou, Nobuaki Nagai, Takao Nishizeki

Research output: Contribution to journalArticlepeer-review

13 Citations (Scopus)


We newly define a generalized vertex-ranking of a graph G as follows: for a positive integer c, a c-vertex-ranking of G is a labeling (ranking) of the vertices of G with integers such that, for any label i, every connected component of the graph obtained from G by deleting the vertices with label > i has at most c vertices with label i. Clearly an ordinary vertex-ranking is a l-vertex-ranking and vice-versa. We present an algorithm to find a c-vertex-ranking of a given tree T using the minimum number of ranks in time O(cn) where n is the number of vertices in T.

Original languageEnglish
Pages (from-to)321-328
Number of pages8
JournalInformation Processing Letters
Issue number6
Publication statusPublished - 1995 Dec 22


  • Algorithms
  • Generalized ranking
  • Graphs
  • Lexicographical order
  • Trees
  • Visible vertices


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