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On the Treewidth and Pathwidth of Permutation Graphs
, 1992
"... In this paper we discuss the problem of finding the treewidth and pathwidth of permutation graphs. If G[r] is a permutation graph with treewidth k, then we show that the pathwidth of G[r] is at most 2k, and we give an algo rithm which constructs a pathdecomposition with width at most 2k in time ..."
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Cited by 54 (14 self)
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In this paper we discuss the problem of finding the treewidth and pathwidth of permutation graphs. If G[r] is a permutation graph with treewidth k, then we show that the pathwidth of G[r] is at most 2k, and we give an algo rithm which constructs a pathdecomposition with width at most 2k
Intrinsically Linked Permutation Graphs
, 2012
"... Inspired by the Petersen graph, Chartrand and Harary in [2] made the following definition: let G and H be graphs on the same number of vertices, and let α be a bijection from the vertices of G to the vertices of H. The αpermutation graph of G and H is the graph formed by taking the disjoint union o ..."
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Inspired by the Petersen graph, Chartrand and Harary in [2] made the following definition: let G and H be graphs on the same number of vertices, and let α be a bijection from the vertices of G to the vertices of H. The αpermutation graph of G and H is the graph formed by taking the disjoint union
I. DOMINATION IN PERMUTATION GRAPHS
"... If i, j belongs to a permutation on n symbols {1, 2, …, p} and i is less than j then there is an edge between i and j in the permutation graph if i appears after j. (i. e) inverse of i is greater than the inverse of j. So the line of i crosses the line of j in the permutation. So there is a one to o ..."
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If i, j belongs to a permutation on n symbols {1, 2, …, p} and i is less than j then there is an edge between i and j in the permutation graph if i appears after j. (i. e) inverse of i is greater than the inverse of j. So the line of i crosses the line of j in the permutation. So there is a one
Boxicity of Permutation Graphs
, 2008
"... An axis parallel ddimensional box is the cartesian product R1 × R2 × · · · × Rd where each Ri is a closed interval on the real line. The boxicity of a graph G, denoted as box(G), is the minimum integer d such that G can be represented as the intersection graph of a collection of ddimensional b ..."
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dimensional boxes: that is two vertices are adjacent if and only if their corresponding boxes intersect. Permutation graphs form a wellknown subclass of perfect graphs. A permutation graph is a graph that can be represented as the intersection graph of a family of line segments that connect two parallel lines
On mapping graphs and permutation graphs
 Math. Solvaca
, 1978
"... We consider finite simple graphs and the terminology of Harary [4] and Behzad—Chartrand [1] is used. Permutation graphs have been studied in several contexts, compare [2, 3]. For completeness we recall the definiton. Let X = (V, E) be a graph with vertexset V={vu..., vn) and edgeset E and p a perm ..."
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Cited by 3 (0 self)
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We consider finite simple graphs and the terminology of Harary [4] and Behzad—Chartrand [1] is used. Permutation graphs have been studied in several contexts, compare [2, 3]. For completeness we recall the definiton. Let X = (V, E) be a graph with vertexset V={vu..., vn) and edgeset E and p a
Polar permutation graphs
, 2009
"... Polar graphs generalise bipartite, cobipartite, and split graphs, and they constitute a special type of matrix partitions. A graph is polar if its vertex set can be partitioned into two, such that one part induces a complete multipartite graph and the other part induces a disjoint union of complete ..."
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Cited by 5 (1 self)
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graphs. Deciding whether a given arbitrary graph is polar, is an NPcomplete problem. Here we show that for permutation graphs this problem can be solved in polynomial time. The result is surprising, as related problems like achromatic number and cochromatic number are NPcomplete on permutation graphs
Coloring Permutation Graphs in Parallel
, 2002
"... A coloring of a graph G is an assignment ofcol]B to its vertices so that no two adjacent vertices have the samecol.]B study theproblP ofcolxxPpermutation graphs using certain properties of thele.Pq representation of a permutation andrel#B[.bEPq between permutations, directed acycld graphs and roo ..."
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Cited by 5 (5 self)
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A coloring of a graph G is an assignment ofcol]B to its vertices so that no two adjacent vertices have the samecol.]B study theproblP ofcolxxPpermutation graphs using certain properties of thele.Pq representation of a permutation andrel#B[.bEPq between permutations, directed acycld graphs
Distance Labeling for Permutation Graphs
, 2005
"... We show that every permutation graph with n elements can be preprocessed in O(n) time, if two linear extensions of the corresponding poset are given, to produce an O(n) space datastructure supporting distance queries in constant time. The datastructure is localized and given as a distance labeling, ..."
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Cited by 1 (0 self)
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We show that every permutation graph with n elements can be preprocessed in O(n) time, if two linear extensions of the corresponding poset are given, to produce an O(n) space datastructure supporting distance queries in constant time. The datastructure is localized and given as a distance labeling
Permutation Bigraphs: An Analogue of Permutation Graphs
, 2011
"... 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, an ..."
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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
Distance and Connectivity Measures in Permutation Graphs
, 2004
"... A permutation graph G π of a graph G (or generalized prism) is obtained by taking two disjoint copies of G and adding an arbitrary matching between the copies. For the parameters diameter, radius, average distance, connectivity and edgeconnectivity, we compare the values of the parameter for G π an ..."
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Cited by 2 (0 self)
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A permutation graph G π of a graph G (or generalized prism) is obtained by taking two disjoint copies of G and adding an arbitrary matching between the copies. For the parameters diameter, radius, average distance, connectivity and edgeconnectivity, we compare the values of the parameter for G π
Results 1  10
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