# Permutation Graphs and Transitive Graphs

@article{Even1972PermutationGA,
title={Permutation Graphs and Transitive Graphs},
author={S. Even and A. Pnueli and A. Lempel},
journal={J. ACM},
year={1972},
volume={19},
pages={400-410}
}
• Published 1972
• Computer Science
• 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
176 Citations
Circular permutation graphs
• Mathematics, Computer Science
• Networks
• 1982
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
• Mathematics, Computer Science
• Inf. Sci.
• 1977
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
• Computer Science, Mathematics
• Theor. Comput. Sci.
• 1987
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
• Mathematics, Computer Science
• Networks
• 1981
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
• Mathematics
• 2019
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
• Mathematics, Computer Science
• Inf. Process. Lett.
• 1995
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
• Mathematics, Computer Science
• FCT
• 1985
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