String graphs. I. The number of critical nonstring graphs is infinite

35Citations
Citations of this article
5Readers
Mendeley users who have this article in their library.

Abstract

String graphs (intersection graphs of curves in the plane) were originally studied in connection with RC-circuits. The family of string graphs is closed in the induced minor order, and so it is reasonable to study critical nonstring graphs (nonstring graphs such that all of their proper induced minors are string graphs). The question of whether there are infinitely many nonisomorphic critical nonstring graphs has been an open problem for some time. The main result of this paper settles this question. In a later paper of this series we show that recognizing string graphs is NP-hard. © 1991.

Cite

CITATION STYLE

APA

Kratochvíl, J. (1991). String graphs. I. The number of critical nonstring graphs is infinite. Journal of Combinatorial Theory, Series B, 52(1), 53–66. https://doi.org/10.1016/0095-8956(91)90090-7

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free