Generalized vertex-rankings of trees

Xiao Zhou, Nobuaki Nagai, Takao Nishizeki

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)

Abstract

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
Volume56
Issue number6
DOIs
Publication statusPublished - 1995 Dec 22

Keywords

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

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Signal Processing
  • Information Systems
  • Computer Science Applications

Fingerprint Dive into the research topics of 'Generalized vertex-rankings of trees'. Together they form a unique fingerprint.

Cite this