Orders: Interval, Interval-Probe, and Interval-k
Document Type
Presentation
Journal/Book Title/Conference
41st Southeastern International Conference on Combinatorics, Graph Theory, and Computing, Boca Raton, FL
Publication Date
2010
Abstract
If an interval graph is such that its complement can be oriented transitively, that orientation yields an interval order. A graph G is an interval-probe graph if its vertices can be partitioned into P (probes) and N (nonprobes) and each vertex v can correspond to an interval Iv so that vertices u and v are adjacent if and only if Iu ∩Iv ̸= Ø and {u,v}∩P ̸= Ø. A graph G is an interval k-graph if its vertices can be properly colored and each vertex v can correspond to an interval Iv so that vertices u and v are adjacent if and only if Iu ∩Iv ̸= Ø and u and v are colored differently. Interval probe graphs generalize interval graphs and interval k-graphs generalize interval-probe graphs. This talk will contain recent characterizations of interval- probe orders (order obtained from a transitive orientation of an interval-probe graph) of interval k-orders (order obtained from a transitive orientation of an interval k-graph).
Recommended Citation
Brown, David E., "Orders: Interval, Interval-Probe, and Interval-k" (2010). Mathematics and Statistics Faculty Presentations. Paper 38.
https://digitalcommons.usu.edu/mathsci_presentations/38