Transactions of the American Mathematical Society · 1982 · 59 citations · 9 references
Natural SciencesComputer ScienceMathematicsCombinatoricsDiscrete MathematicsSet TheoryCombinatorial EnumerationCombinatorial Set TheoryEnumerative CombinatoricsGraph AlgorithmsGraph TheoryTopological CombinatoricsEnumeration Algorithms For GraphsEnumerative Graph TheoryGraph EnumerationInterval-based RepresentationStructural DecompositionStructural Decomposition Analysis
In this paper we enumerate interval graphs (up to isomorphism) along with labelled interval graphs, identity interval graphs, transitive interval graphs and various sorts of unit interval graphs. The enumeration makes use of a structural decomposition of interval graphs which leads to a characterization of those interval graphs having a unique interval representation. Several tables are included.
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Asymptotic Methods in Enumeration
Edward A. Bender · SIAM Review · 1974 · 458 citations
Proof Techniques in Graph Theory
N. J. A. Sloane, Frank Harary · Mathematics of Computation · 1970 · 385 citations
On double and multiple interval graphs
William T. Trotter, Frank Harary · Journal of Graph Theory · 1979 · 112 citations