Intersection graph of unit intervals on the real number line
An indifference graph, formed from a set of points on the real line by connecting pairs of points whose distance is at most one
In graph theory, a branch of mathematics, an indifference graph is an undirected graph constructed by assigning a real number to each vertex and connecting two vertices by an edge when their numbers are within one unit of each other.[1] Indifference graphs are also the intersection graphs of sets of unit intervals, or of properly nested intervals (intervals none of which contains any other one). Based on these two types of interval representations, these graphs are also called unit interval graphs or proper interval graphs; they form a subclass of the interval graphs.
^Roberts, Fred S. (1969), "Indifference graphs", Proof Techniques in Graph Theory (Proc. Second Ann Arbor Graph Theory Conf., Ann Arbor, Mich., 1968), Academic Press, New York, pp. 139–146, MR 0252267.
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circle graphs as a special case. Every distance-hereditary graph is a circle graph, as is every permutation graph and every indifferencegraph. Every...
intersection graph of intervals on the real line, or of connected subgraphs of a path graph. An indifferencegraph may be defined as the intersection graph of unit...
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threshold graphs can be recognized in linear time; if a graph is not threshold, an obstruction (one of P4, C4, or 2K2) will be output. Indifferencegraph Series–parallel...
joins points of equal value. It is a plane section of the three-dimensional graph of the function f ( x , y ) {\displaystyle f(x,y)} parallel to the ( x ...
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proved by Alvin Roth. When the preferences are strict (there are no indifferences), TTC always finds a strictly Pareto-efficient allocation. Moreover...
MR 0498294. Roberts, Fred S. (1969), "Indifferencegraphs", Proof Techniques in Graph Theory (Proc. Second Ann Arbor Graph Theory Conf., Ann Arbor, Mich., 1968)...
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James Choi states that this deviates from the advice of economists. The graph below illustrates the expected utility model, in which U(c) is increasing...
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of variables and their conditional dependencies via a directed acyclic graph (DAG). While it is one of several forms of causal notation, causal networks...
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