Rankings of directed graphs

Jan Kratochvíl, Zsolt Tuza

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

A ranking of a graph is a coloring of the vertex set with positive integers such that on every path connecting two vertices of the same color there is a vertex of larger color. We consider the directed variant of this problem, where the above condition is imposed only on those paths in which all edges are oriented in the same direction. We show that the ranking number of a directed tree is bounded by that of its longest directed path plus one, and that it can be computed in polynomial time. Unlike the undirected case, however, deciding whether the ranking number of a directed (and even of an acyclic directed) graph is bounded by a constant is NP-complete. In fact, the 3-ranking of planar bipartite acyclic digraphs is already hard.

Original languageEnglish
Title of host publicationGraph-Theoretic Concepts in Computer Science - 24th International Workshop, WG 1998, Proceedings
EditorsJuraj Hromkovic, Ondrej Sykora
PublisherSpringer Verlag
Pages114-123
Number of pages10
ISBN (Print)3540651950, 9783540651956
DOIs
Publication statusPublished - 1998
Event24th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 1998 - Smolenice Castle, Slovakia
Duration: Jun 18 1998Jun 20 1998

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume1517
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other24th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 1998
CountrySlovakia
CitySmolenice Castle
Period6/18/986/20/98

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Fingerprint Dive into the research topics of 'Rankings of directed graphs'. Together they form a unique fingerprint.

  • Cite this

    Kratochvíl, J., & Tuza, Z. (1998). Rankings of directed graphs. In J. Hromkovic, & O. Sykora (Eds.), Graph-Theoretic Concepts in Computer Science - 24th International Workshop, WG 1998, Proceedings (pp. 114-123). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1517). Springer Verlag. https://doi.org/10.1007/10692760_10