Permutation Graphs and Transitive Graphs

  title={Permutation Graphs and Transitive Graphs},
  author={S. Even and A. Pnueli and A. Lempel},
  journal={J. ACM},
A graph G with vertex set N = {1, 2, .-. [...] Key Method , n} is called a permutation graph there exists a permutation P on N such that for i , j E N, (i j)[P-'(i) P-'(j)] < 0 if ar only if i and j are joined by an edge in G. A structural relationship is established between permutation graphs and transitive graph An algorithm for determining whether a given graph is a permutation graph is given. Efficie, algorithms for finding a maximum size clique and a minimum coloration of transitive grapl are presented…Expand
Circular permutation graphs
A new class of intersection graphs called circular permutation graphs is introduced and characterized which leads to a recognition algorithm which requires O(δ|E|) steps where δ is the maximum degree of a vertex. Expand
Efficient algorithms for (3, 1) graphs
It is shown that there exists a linear algorithm for constructing a Hamiltonian circuit in a connected (3, 1) graph and an n 4 -algorithm for finding a minimum coloring in a (3-1) graph. Expand
CHAPTER 7 – Permutation Graphs
Publisher Summary This chapter discusses a class of perfect graphs—permutation graphs—which has a large number of applications. An undirected graph G is called a permutation graph if there exists aExpand
Chapter 7 – Permutation graphs
Publisher Summary This chapter presents a class of perfect graphs, which has a large number of applications. An undirected graph G[Π] from Π can be constructed in the following manner: G[Π] hasExpand
On the maximum stable set of a permutation graph
The domination problems in permutation graphs were studied by Farber and Keil and Golumbic showed an 0(n log n) algorithm to find the chromatic number C(G), which is the cardinality of maximum stable set. Expand
On Domination Problems for Permutation and Other Graphs
An algorithm with time bound O ( n 2 ) for the weighted independent domination problem on permutation graphs and an investigation of (weighted) dominating clique problems for several graph classes including an NP-completeness result for weakly triangulated graphs as well as polynomial time bounds are given. Expand
Finding maximum cliques in circle graphs
An algorithm which requires O(n2) steps to generate one maximum clique is presented and the algorithm can also be used to generate all maximum cliques where the number of steps need to generate each additional maximumClique is linear in its size. Expand
A study on random permutation graphs
For a given permutation $\pi_n$ in $S_n$, a random permutation graph is formed by including an edge between two vertices $i$ and $j$ if and only if $(i - j) (\pi_n(i) - \pi_n (j)) < 0$. In thisExpand
An O(log n) Parallel Algorithm for Constructing a Spanning Tree on Permutation Graphs
An O(log n) time parallel algorithm with O( n log n ) processors on the EREW PRAM for constructing a spanning tree on an unweighted permutation graph. Expand
On the restriction of some NP-complete graph problems to permutation graphs
Permutation graphs are known as a useful class of perfect graphs for which the NP-complete graph problems GRAPH k-COLORABILITY, PARTITION INTO CLIQUES, CLIQUE and INDEPENDENT SET (VERTEX COVER)Expand


Transitive Orientation of Graphs and Identification of Permutation Graphs
The graphs considered in this paper are assumed to be finite, with no edge joining a vertex to itself and with no two distinct edges joining the same pair of vertices. An undirected graph will beExpand
Minimizing the Number of States in Incompletely Specified Sequential Switching Functions
A partially enumerative solution to the problem of reducing the number of rows in a flow table in which some of the entries are unspecified is presented and a rough indication of the efficiency of the given procedures is obtained. Expand
The Art of Computer Programming
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