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• # Artykuł - szczegóły

## Discussiones Mathematicae Graph Theory

2014 | 34 | 2 | 353-359

## The niche graphs of interval orders

EN

### Abstrakty

EN
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

EN

353-359

wydano
2014-05-01
online
2014-04-12

### Twórcy

autor
• Department of Mathematics Pusan National University Busan 609-735, Korea
autor
• Division of Information Engineering Faculty of Engineering, Information and Systems University of Tsukuba Ibaraki 305-8573, Japan

### Bibliografia

•  C. Cable, K.F. Jones, J.R. Lundgren and S. Seager, Niche graphs, Discrete Appl. Math. 23 (1989) 231-241. doi:10.1016/0166-218X(89)90015-2[Crossref]
•  J.E. Cohen, Interval graphs and food webs. A finding and a problem, RAND Corpo- ration, Document 17696-PR, Santa Monica, California (1968).
•  P.C. Fishburn, Interval Orders and Interval Graphs: A Study of Partially Ordered Sets, Wiley-Interscience Series in Discrete Mathematics, A Wiley-Interscience Pub- lication (John Wiley & Sons Ltd., Chichester, 1985).
•  S.-R. Kim and F.S. Roberts, Competition graphs of semiorders and Conditions C(p) and C∗(p), Ars Combin. 63 (2002) 161-173.
•  Y. Sano, The competition-common enemy graphs of digraphs satisfying conditions C(p) and C′(p), Congr. Numer. 202 (2010) 187-194.
•  D.D. Scott, The competition-common enemy graph of a digraph, Discrete Appl. Math. 17 (1987) 269-280. doi:10.1016/0166-218X(87)90030-8[Crossref]

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