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45
ON PERMUTATION CLIQUES
, 1980
"... The symmetric group S, is a metric space with distance d(a, b) = IE(a'b) ( where E(c) is the set of points moved by c E S,. Let L be a given subset of {I. 2,..., n}, a permutation clique A = A(L, n) is any subset A c S, with d(a, b)EL whenever a, b EA, a # b. We give a framework of new and kn ..."
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Cited by 2 (2 self)
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The symmetric group S, is a metric space with distance d(a, b) = IE(a'b) ( where E(c) is the set of points moved by c E S,. Let L be a given subset of {I. 2,..., n}, a permutation clique A = A(L, n) is any subset A c S, with d(a, b)EL whenever a, b EA, a # b. We give a framework of new
On the Linear Structure and CliqueWidth of Bipartite Permutation Graphs
, 2001
"... Bipartite permutation graphs have several nice characterizations in terms of vertex ordering. Besides, as ATfree graphs, they have a linear structure in the sense that any connected bipartite permutation graph has a dominating path. In the present paper, we elaborate the linear structure of bipa ..."
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Cited by 18 (4 self)
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of bipartite permutation graphs by showing that any connected graph in the class can be stretched into a "path" with "edges" being chain graphs. A particular consequence from the obtained characterization is that the cliquewidth of bipartite permutation graphs is unbounded, which
LINEAR CLIQUEWIDTH FOR SUBCLASSES OF COGRAPHS, WITH CONNECTIONS TO PERMUTATIONS
, 2013
"... We prove that a hereditary property of cographs has bounded linear cliquewidth if and only if it does not contain all quasithreshold graphs or their complements. The proof borrows ideas from the enumeration of permutation classes, and the similarities between these two strands of investigation lead ..."
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lead us to a conjecture relating the graph properties of bounded linear cliquewidth to permutation classes with rational generating functions which would have farreaching consequences if true.
Longest common subsequences in permutations and maximum cliques in circle graphs
 In Proceedings of CPM
, 2006
"... Abstract. For two strings a, b, the longest common subsequence (LCS) problem consists in comparing a and b by computing the length of their LCS. In a previous paper, we defined a generalisation, called “the all semilocal LCS problem”, for which we proposed an efficient output representation and an ..."
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Cited by 7 (3 self)
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and an efficient algorithm. In this paper, we consider a restriction of this problem to strings that are permutations of a given set. The resulting problem is equivalent to the all local longest increasing subsequences (LIS) problem. We propose an algorithm for this problem, running in time O(n 1.5) on an input
WellQuasiOrder for Permutation Graphs Omitting a Path and a Clique
"... We consider wellquasiorder for classes of permutation graphs which omit both a path and a clique. Our principle result is that the class of permutation graphs omitting P5 and a clique of any size is wellquasiordered. This is proved by giving a structural decomposition of the corresponding permut ..."
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We consider wellquasiorder for classes of permutation graphs which omit both a path and a clique. Our principle result is that the class of permutation graphs omitting P5 and a clique of any size is wellquasiordered. This is proved by giving a structural decomposition of the corresponding
Cell Flipping in Permutation Diagrams
, 2001
"... Permutation diagrams have been used in circuit design to model a set of single point nets crossing a channel, where the minimum number of layers needed to realize the diagram equals the clique number !(G) of its permutation graph, the value of which can be calculated in O(n log n) time. We consider ..."
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Permutation diagrams have been used in circuit design to model a set of single point nets crossing a channel, where the minimum number of layers needed to realize the diagram equals the clique number !(G) of its permutation graph, the value of which can be calculated in O(n log n) time. We consider
On the Longest Upsequence Problem for Permutations
, 1999
"... Given a permutation of n numbers, its longest upsequence can be found in time O(n log log n). Finding the longest upsequence (resp. longest downsequence) of a permutation solves the maximum independent set problem (resp. the clique problem) for the corresponding permutation graph. Moreover, we discu ..."
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Cited by 3 (0 self)
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Given a permutation of n numbers, its longest upsequence can be found in time O(n log log n). Finding the longest upsequence (resp. longest downsequence) of a permutation solves the maximum independent set problem (resp. the clique problem) for the corresponding permutation graph. Moreover, we
A new genetic algorithm for minimum span frequency assignment using permutation and clique
 Proc. of Genetic and Evolutionary Computation Conference 2000 (GECCO2000
, 2000
"... We propose a new Genetic Algorithm (GA) for solving the minimum span frequency assignment problem (MSFAP). The MSFAP is minimizing the range of the frequencies assigned to each transmitter in a region satisfying a number of constraints. The proposed method involves finding and ordering of the trans ..."
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Cited by 1 (1 self)
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We propose a new Genetic Algorithm (GA) for solving the minimum span frequency assignment problem (MSFAP). The MSFAP is minimizing the range of the frequencies assigned to each transmitter in a region satisfying a number of constraints. The proposed method involves finding and ordering of the transmitters for use in a greedy (sequential) assignment process, and it also utilizes graph theoretic constraint to reduce search space. Results are given which show that our GA produces optimal solutions to several practical problems, and the performance of our GA is far better than the existing GAs. 1
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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in the Euclidean plane. Let G be a permutation graph with chromatic number χ(G) and maximum clique size ω(G). We will show that box(G) ≤ χ(G) = ω(G) and this bound is tight.
Splittings and Ramsey properties of permutation classes
 arXiv:1307.0027 [math.CO]. Cited on
"... We say that a permutation pi is merged from permutations ρ and τ, if we can color the elements of pi red and blue so that the red elements are orderisomorphic to ρ and the blue ones to τ. A permutation class is a set of permutations closed under taking subpermutations. A permutation class C is spli ..."
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Cited by 1 (0 self)
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of certain permutation classes and colorings of circle graphs of bounded clique size. Indeed, our splittability results can be interpreted as a generalization of a theorem of Gyárfás stating that circle graphs of bounded clique size have bounded chromatic number. 1
Results 1  10
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45