Rankings of directed graphs

Jan Kratochvíl, Z. 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 publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
PublisherSpringer Verlag
Pages114-123
Number of pages10
Volume1517
ISBN (Print)3540651950, 9783540651956
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)03029743
ISSN (Electronic)16113349

Other

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

Fingerprint

Directed graphs
Directed Graph
Ranking
Color
Coloring
Path
Polynomials
Acyclic Digraph
Directed Acyclic Graph
Vertex of a graph
Colouring
Polynomial time
NP-complete problem
Integer
Graph in graph theory

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Kratochvíl, J., & Tuza, Z. (1998). Rankings of directed graphs. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 1517, pp. 114-123). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1517). Springer Verlag.

Rankings of directed graphs. / Kratochvíl, Jan; Tuza, Z.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 1517 Springer Verlag, 1998. p. 114-123 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1517).

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

Kratochvíl, J & Tuza, Z 1998, Rankings of directed graphs. in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). vol. 1517, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 1517, Springer Verlag, pp. 114-123, 24th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 1998, Smolenice Castle, Slovakia, 6/18/98.
Kratochvíl J, Tuza Z. Rankings of directed graphs. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 1517. Springer Verlag. 1998. p. 114-123. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
Kratochvíl, Jan ; Tuza, Z. / Rankings of directed graphs. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 1517 Springer Verlag, 1998. pp. 114-123 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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