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
@article{bwmeta1.element.doi-10_7151_dmgt_1741,
author = {Jeongmi Park and Yoshio Sano},
title = {The niche graphs of interval orders},
journal = {Discussiones Mathematicae Graph Theory},
volume = {34},
year = {2014},
pages = {353-359},
zbl = {1290.05124},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_7151_dmgt_1741}
}
Jeongmi Park; Yoshio Sano. The niche graphs of interval orders. Discussiones Mathematicae Graph Theory, Tome 34 (2014) pp. 353-359. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_7151_dmgt_1741/
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