On the restriction of some NP-complete graph problems to permutation graphs

2006 ◽  
pp. 53-62 ◽  
Author(s):  
Andreas Brandstädt ◽  
Dieter Kratsch
Keyword(s):  
Complete Graph ◽  
Permutation Graphs ◽  
Graph Problems ◽  
Np Complete

Efficient DNA sticker algorithms for NP-complete graph problems

2002 ◽  
Vol 144 (3) ◽  
pp. 297-309 ◽  
Author(s):  
Karl-Heinz Zimmermann
Keyword(s):  
Complete Graph ◽  
Graph Problems ◽  
Np Complete

A note on "Some simplified NP-complete graph problems"

1977 ◽  
Vol 9 (3) ◽  
pp. 24-24 ◽  
Author(s):  
M. S. Krishnamoorthy
Keyword(s):  
Complete Graph ◽  
Graph Problems ◽  
Np Complete

scholarly journals Some simplified NP-complete graph problems

1976 ◽  
Vol 1 (3) ◽  
pp. 237-267 ◽  
Author(s):  
M.R. Garey ◽  
D.S. Johnson ◽  
L. Stockmeyer
Keyword(s):  
Complete Graph ◽  
Graph Problems ◽  
Np Complete

Parallel bioinspired algorithms for NP complete graph problems

2009 ◽  
Vol 69 (3) ◽  
pp. 221-229 ◽  
Author(s):  
Israel Marck Martínez-Pérez ◽  
Karl-Heinz Zimmermann
Keyword(s):  
Complete Graph ◽  
Graph Problems ◽  
Np Complete ◽  
Bioinspired Algorithms

A note on "A note on 'Some simplified NP-complete graph problems'"

1978 ◽  
Vol 9 (4) ◽  
pp. 17-17 ◽  
Author(s):  
M. R. Garey ◽  
D. S. Johnson
Keyword(s):  
Complete Graph ◽  
Graph Problems ◽  
Np Complete

COMPUTING THE RUPTURE DEGREE IN COMPOSITE GRAPHS

2010 ◽  
Vol 21 (03) ◽  
pp. 311-319 ◽  
Author(s):  
AYSUN AYTAC ◽  
ZEYNEP NIHAN ODABAS
Keyword(s):  
Complete Graph ◽  
Connected Graph ◽  
The Other ◽  
Trade Off ◽  
Number Of Components ◽  
Np Complete ◽  
Work Done ◽  
Better Than

The rupture degree of an incomplete connected graph G is defined by [Formula: see text] where w(G - S) is the number of components of G - S and m(G - S) is the order of a largest component of G - S. For the complete graph Kn, rupture degree is defined as 1 - n. This parameter can be used to measure the vulnerability of a graph. Rupture degree can reflect the vulnerability of graphs better than or independent of the other parameters. To some extent, it represents a trade-off between the amount of work done to damage the network and how badly the network is damaged. Computing the rupture degree of a graph is NP-complete. In this paper, we give formulas for the rupture degree of composition of some special graphs and we consider the relationships between the rupture degree and other vulnerability parameters.

EDGE-DELETION GRAPH PROBLEMS WITH FIRST-ORDER EXPRESSIBLE SUBGRAPH PROPERTIES

1991 ◽  
Vol 02 (02) ◽  
pp. 83-99
Author(s):  
V. ARVIND ◽  
S. BISWAS
Keyword(s):  
Normal Form ◽  
Polynomial Time ◽  
Edge Deletion ◽  
Present Evidence ◽  
First Order ◽  
Graph Problems ◽  
Polynomial Time Algorithms ◽  
Complete Problems ◽  
Np Complete ◽  
New Perspective

In this paper edge-deletion problems are studied with a new perspective. In general an edge-deletion problem is of the form: Given a graph G, does it have a subgraph H obtained by deleting zero or more edges such that H satisfies a polynomial-time verifiable property? This paper restricts attention to first-order expressible properties. If the property is expressed by π, which in prenex normal form is Q(Φ) where Q is the quantifier-prefix, then we prove results on the quantifier structure that characterize the complexity of the edge-deletion problem. In particular we give polynomial-time algorithms for problems for which Q is ‘simple’ and in other cases we encode certain NP-complete problems as edge-deletion problems, essentially using the quantifier structure of π. We also present evidence that Q alone cannot capture the complexity of the edge-deletion problem.

scholarly journals On bipartite powers of bigraphs

2012 ◽  
Vol Vol. 14 no. 2 (Graph Theory) ◽  
Author(s):  
Yoshio Okamoto ◽  
Yota Otachi ◽  
Ryuhei Uehara
Keyword(s):  
Graph Theory ◽  
Permutation Graphs ◽  
International Audience ◽  
Bipartite Permutation Graphs ◽  
Np Complete

Graph Theory International audience The notion of graph powers is a well-studied topic in graph theory and its applications. In this paper, we investigate a bipartite analogue of graph powers, which we call bipartite powers of bigraphs. We show that the classes of bipartite permutation graphs and interval bigraphs are closed under taking bipartite power. We also show that the problem of recognizing bipartite powers is NP-complete in general.

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