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The niche graphs of interval orders

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Park J., Sano Y.

Discussiones Mathematicae Graph Theory

2014

tom 34

nr 2

353-359

The niche graph of a digraph D is the (simple undirected) graph which has the same vertex set as D and has an edge between two distinct vertices x and y if and only if N+D(x) ∩ N+D(y) ≠ ∅ or N−D(x) ∩ N−D(y) ≠ ∅, where N+D(x) (resp. N−D(x)) is the set of out-neighbors (resp. in-neighbors) of x in D. A digraph D = (V,A) is called a semiorder (or a unit interval order ) if there exist a real-valued function f : V → R on the set V and a positive real number δ ∈ R such that (x, y) ∈ A if and only if f(x) > f(y)+δ. A digraph D = (V,A) is called an interval order if there exists an assignment J of a closed real interval J(x) ⊂ R to each vertex x ∈ V such that (x, y) ∈ A if and only if min J(x) > max J(y). Kim and Roberts characterized the competition graphs of semiorders and interval orders in 2002, and Sano characterized the competition-common enemy graphs of semiorders and interval orders in 2010. In this note, we give characterizations of the niche graphs of semiorders and interval orders

Ograniczanie wyników

1 Discussiones Mathematicae Graph Theory

1 Park J.

1 Sano Y.

1 2014

Wyniki wyszukiwania

The niche graphs of interval orders