New characterizations of proper interval bigraphs
نویسندگان
چکیده
A proper interval bigraph is a bigraph where to each vertex we can assign a closed interval such that the intervals can be chosen to be inclusion free and vertices in the opposite partite sets are adjacent when the corresponding intervals intersect. In this paper, we introduce the notion of astral triple of edges and along the lines of characterization of interval graphs via the absence of asteroidal triple of vertices we characterize proper interval bigraphs via the absence of astral triple of edges. We also characterize proper interval bigraphs in terms of dominating pair of vertices as defined by Corneil et al. Tucker characterized proper circular arc graphs in terms of circularly compatible 1’s of adjacency matrices. Sen and Sanyal characterized adjacency matrices of proper interval bigraphs in terms of monotone consecutive arrangement. We have shown an interrelation between these two concepts. c ⃝ 2015 Kalasalingam University. Production and Hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
منابع مشابه
Permutation bigraphs and interval containments
A bipartite graph with partite sets X and Y is a permutation bigraph if there are two linear orderings of its vertices so that xy is an edge for x ∈ X and y ∈ Y if and only if x appears later than y in the first ordering and earlier than y in the second ordering. We characterize permutation bigraphs in terms of representations using intervals. We determine which permutation bigraphs are interva...
متن کاملPermutation Bigraphs: An Analogue of Permutation Graphs
We introduce the class of permutation bigraphs as an analogue of permutation graphs. We show that this is precisely the class of bigraphs having Ferrers dimension at most 2. We also characterize the subclasses of interval bigraphs and indifference bigraphs in terms of their permutation labelings, and we relate permutation bigraphs to posets of dimension 2.
متن کاملMinimum Cost Homomorphisms to Proper Interval Graphs and Bigraphs
For graphs G and H , a mapping f : V (G)→V (H) is a homomorphism of G to H if uv ∈ E(G) implies f(u)f(v) ∈ E(H). If, moreover, each vertex u ∈ V (G) is associated with costs ci(u), i ∈ V (H), then the cost of the homomorphism f is ∑ u∈V (G) cf(u)(u). For each fixed graph H , we have the minimum cost homomorphism problem, written as MinHOM(H). The problem is to decide, for an input graph G with ...
متن کاملOn bipartite powers of bigraphs
The notion of graph powers is a well-studied topic in graph theory and its applications. In this paper, we investigate a bipartite analogue of graph powers, which we call bipartite powers of bigraphs. We show that the classes of bipartite permutation graphs and interval bigraphs are closed under taking bipartite power. We also show that the problem of recognizing bipartite powers is NP-complete...
متن کاملQuasimonotone graphs
For any class C of bipartite graphs, we define quasi-C to be the class of all graphs G such that every bipartition of G belongs to C. This definition is motivated by a generalisation of the switch Markov chain on perfect matchings from bipartite graphs to nonbipartite graphs. The monotone graphs, also known as bipartite permutation graphs and proper interval bigraphs, are such a class of bipart...
متن کامل