# 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} }

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

- Mathematics
- 1980

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 a… Expand

Chapter 7 – Permutation graphs

- Mathematics
- 2004

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] has… Expand

On the maximum stable set of a permutation graph

- Computer Science
- ACM-SE 28
- 1990

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 this… Expand

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

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