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In graph theory, an interval graph is an undirected graph formed from a set of intervals on the real line, with a vertex for each interval and an edge between vertices whose intervals intersect. It is the intersection graph of the intervals.
The edges of the graph are d-tuples of intervals, one interval in every real line. [1] The simplest case is d = 1. The vertex set of a 1-interval hypergraph is the set of real numbers; each edge in such a hypergraph is an interval of the real line. For example, the set { [−2, −1], [0, 5], [3, 7] } defines a 1-interval
In the mathematical discipline of graph theory, the line graph of an undirected graph G is another graph L(G) that represents the adjacencies between edges of G. L(G) is constructed in the following way: for each edge in G, make a vertex in L(G); for every two edges in G that have a vertex in common, make an edge between their corresponding vertices in L(G).
quasi-line graph A quasi-line graph or locally co-bipartite graph is a graph in which the open neighborhood of every vertex can be partitioned into two cliques. These graphs are always claw-free and they include as a special case the line graphs. They are used in the structure theory of claw-free graphs. quasi-random graph sequence
This equivalence between pathwidth and interval thickness is closely analogous to the equivalence between treewidth and the minimum clique number (minus one) of a chordal graph of which the given graph is a subgraph. Interval graphs are a special case of chordal graphs, and chordal graphs can be represented as intersection graphs of subtrees of ...
A d-claw in a graph is a set of d+1 vertices, one of which (the "center") is connected to the other d vertices, but the other d vertices are not connected to each other. A d-claw-free graph is a graph that does not have a d-claw subgraph. Consider the algorithm that starts with an empty set, and incrementally adds an arbitrary vertex to it as ...
A graph constructed from a multigraph by replacing each edge by a fuzzy linear interval graph. This generalizes the construction of a line graph, in which every edge of the multigraph is replaced by a vertex. Fuzzy linear interval graphs are constructed in the same way as fuzzy circular interval graphs, but on a line rather than on a circle.
ABA is an applied science devoted to developing procedures which will produce observable changes in behavior. [3] [9] It is to be distinguished from the experimental analysis of behavior, which focuses on basic experimental research, [10] but it uses principles developed by such research, in particular operant conditioning and classical conditioning.