Intersection Dimensions of Graph Classes

Jan Kratochvil, Z. Tuza

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

The intersection dimension of a graph G with respect to a class A of graphs is the minimum k such that G is the intersection of at most k graphs on vertex set V(G) each of which belongs to A. We consider the question when the intersection dimension of a certain family of graphs is bounded or unbounded. Our main results are (1) if A is hereditary, i.e., closed on induced subgraphs, then the intersection dimension of all graphs with respect to A is unbounded, and (2) the intersection dimension of planar graphs with respect to the class of permutation graphs is bounded. We also give a simple argument based on [Ben-Arroyo Hartman, I., Newman, I., Ziv, R.: On grid intersection graphs, Discrete Math. 87 (1991) 41-52] why the boxicity (i.e., the intersection dimension with respect to the class of interval graphs) of planar graphs is bounded. Further we study the relationships between intersection dimensions with respect to different classes of graphs.

Original languageEnglish
Pages (from-to)159-168
Number of pages10
JournalGraphs and Combinatorics
Volume10
Issue number2
DOIs
Publication statusPublished - 1994

Fingerprint

Graph Classes
Intersection
Graph in graph theory
Planar graph
Boxicity
Permutation Graphs
Grid Graph
Interval Graphs
Intersection Graphs
Induced Subgraph
Closed
Class
Vertex of a graph

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Theoretical Computer Science

Cite this

Intersection Dimensions of Graph Classes. / Kratochvil, Jan; Tuza, Z.

In: Graphs and Combinatorics, Vol. 10, No. 2, 1994, p. 159-168.

Research output: Contribution to journalArticle

Kratochvil, Jan ; Tuza, Z. / Intersection Dimensions of Graph Classes. In: Graphs and Combinatorics. 1994 ; Vol. 10, No. 2. pp. 159-168.
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