Intersection graphs of curves in the plane

G. Ehrlich, S. Even, R. E. Tarjan

Research output: Contribution to journalArticle

91 Scopus citations

Abstract

Let V be a set of curves in the plane. The corresponding intersection graph has V as the set of vertices, and two vertices are connected by an edge if and only if the two corresponding curves intersect in the plane. It is shown that the set of intersection graphs of curves in the plane is a proper subset of the set of all undirected graphs. Furthermore, the set of intersection graphs of straight line-segments is a proper subset of the set of the intersection graphs of curves in the plane. Finally, it is shown that for every k ≥ 3, the problem of determining whether an intersection graph of straight line-segments is k-colorable is NP-complete.

Original languageEnglish (US)
Pages (from-to)8-20
Number of pages13
JournalJournal of Combinatorial Theory, Series B
Volume21
Issue number1
DOIs
StatePublished - Aug 1976
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics

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