String graph: Difference between revisions

Revision as of 20:04, 15 July 2011

Revision as of 15:13, 8 November 2011

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== Background ==

{{harvs|txt|last=Benzer|first=Seymour|authorlink=Seymour Benzer|year=1959}} described a concept similar to string graphs as they applied to genetic structures. In that context, he also posed the specific case of intersecting intervals on a line, namely the now classical family of [[interval graph]]s. Later, {{harvtxt|Sinden|1966}} specified the same idea to electrical networks and printed circuits. The mathematical study of string graphs began with the paper {{harvtxt|Ehrlich|Even|Tarjan|1976}} and

through a collaboration between Sinden and [[Ronald Graham]], where the characterization of string graphs eventually came to be posed as an open question at the 5^th5th Hungarian Colloquium on Combinatorics in 1976.<ref>{{harvtxt|Graham|1976}}.</ref> However, the recognition of string graphs was eventually proven to be [[NP-complete]], implying that no simple characterization is likely to exist.<ref>{{harvtxt|Kratochvil|1991}} showed string graph recognition to be NP-hard, but were not able to show that it could be solved in NP. After intermediate results by {{harvtxt|Schaefer|Štefankovič|2001}} and {{harvtxt|Pach|Tóth|2002}}, {{harvtxt|Schaefer|Sedgwick|Štefankovič|2003}} completed the proof that the problem is NP-complete.</ref>

==Related graph classes==

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| first1 = Marcus | last1 = Schaefer | first2 = Daniel | last2 = Štefankovič

| title = Decidability of string graphs

| journal = [[Symposium on Theory of Computing|Proceedings of the 33^rd33rd Annual ACM Symposium on the Theory of Computing (STOC 2001)]]

| year = 2001

| pages = 241–246}}.