منابع مشابه
On opposition graphs, coalition graphs, and bipartite permutation graphs
A graph is an opposition graph, respectively, a coalition graph, if it admits an acyclic orientation which puts the two end-edges of every chordless 4-vertex path in opposition, respectively, in the same direction. Opposition and coalition graphs have been introduced and investigated in connection to perfect graphs. Recognizing and characterizing opposition and coalition graphs still remain lon...
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 کاملThe Longest Path Problem on Permutation Graphs
The longest path problem on graph G is a classic problem which is to find a simple path such that the number of vertices of the path is maximum among all possible paths of G. In this paper, we show that the longest path problem can be solved in linear time on permutation graphs.
متن کاملSliding Token on Bipartite Permutation Graphs
Sliding Token is a natural reconfiguration problem in which vertices of independent sets are iteratively replaced by neighbors. We develop techniques that may be useful in answering the conjecture that Sliding Token is polynomial-time decidable on bipartite graphs. Along the way, we give efficient algorithms for Sliding Token on bipartite permutation and bipartite distance-hereditary graphs.
متن کاملOn random trees obtained from permutation graphs
A permutation w gives rise to a graph Gw; the vertices of Gw are the letters in the permutation and the edges of Gw are the inversions of w. We find that the number of trees among permutation graphs with n vertices is 2n−2 for n ≥ 2. We then study Tn, a uniformly random tree from this set of trees. In particular, we study the number of vertices of a given degree in Tn, the maximum degree in Tn,...
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ژورنال
عنوان ژورنال: Journal of the Egyptian Mathematical Society
سال: 2012
ISSN: 1110-256X
DOI: 10.1016/j.joems.2012.08.008