layered graph

(definition)

Definition: A connected graph where "layers" L₀ … L_k partition the vertices. Each edge, which has a nonnegative integral weight, connects only vertices in successive layers. The width is the greatest number of vertices in any layer, i.e., MAX_i=0^k |L_i|.

Generalization (I am a kind of ...)
connected graph.

Specialization (... is a kind of me.)
bipartite graph.

Note: A bipartite graph is a layered graph with two layers.

A. Fiat, D.P. Foster, H.J. Karloff, Y. Rabani, Y. Ravid, and S. Vishwanathan. Competitive Algorithms for Layered Graph Traversal. SIAM J. Comput., to appear. Preliminary version appeared in FOCS '91. Contributed by Giovanni Fiaschi <Giovanni.Fiaschi@marconi.com> June 2000.

Author: PEB

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Entry modified 11 April 2005.
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Cite this as:
Paul E. Black, "layered graph", in Dictionary of Algorithms and Data Structures [online], Paul E. Black, ed. 11 April 2005. (accessed TODAY) Available from: https://www.nist.gov/dads/HTML/layeredgraph.html