This paper explores the intimate connection between finite interval graphs and interval orders. Special attention is given to the family of interval orders that agree with, or provide representations of, an interval graph. Two characterizations (one by P. Hanlon) of interval graphs with essentially
Combinatorial Aspects of Interval Orders and Interval Graphs
โ Scribed by William T. Trotter
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 28 KB
- Volume
- 2
- Category
- Article
- ISSN
- 1571-0653
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โฆ Synopsis
We survey recent research on combinatorial properties of interval orders and interval graphs. Topics include: optimization with an uncooperative partner, ramsey trails, sorting with partial information, tree width and graph decompositions, combinatorial extremal problems, shift graphs, Dedekind's enumeration problem, and dynamic storage allocation. We relate these themes to the classical applications of interval orders as models of imprecise data.
๐ SIMILAR VOLUMES
Let sk(n) be the largest integer such that every n-point interval order with NO antichain of more than k points includes an Sk(n)-point 'semiorder. When k = 1, s,(n) = n since all interval ordexs with no two-point antichains are ch:&s.
A symmetric, anfireflexive relation S is a comparability graph ff one can assign a transitive orientation to the edges: we obtain a partial order. We say that S is a comparability graph with constraint C, a subrelation of S, if S has a transitive orientation including C. A characterization is given