Related Concepts
An order-theoretic analog to the intersection graphs are the containment orders. In the same way that an intersection representation of a graph labels every vertex with a set so that vertices are adjacent if and only if their sets have nonempty intersection, so a containment representation f of a poset labels every element with a set so that for any x and y in the poset, x ≤ y if and only if f(x) ⊆ f(y).
Read more about this topic: Intersection Graph
Famous quotes containing the words related and/or concepts:
“The near explains the far. The drop is a small ocean. A man is related to all nature. This perception of the worth of the vulgar is fruitful in discoveries. Goethe, in this very thing the most modern of the moderns, has shown us, as none ever did, the genius of the ancients.”
—Ralph Waldo Emerson (1803–1882)
“During our twenties...we act toward the new adulthood the way sociologists tell us new waves of immigrants acted on becoming Americans: we adopt the host culture’s values in an exaggerated and rigid fashion until we can rethink them and make them our own. Our idea of what adults are and what we’re supposed to be is composed of outdated childhood concepts brought forward.”
—Roger Gould (20th century)