## 2,126 Citations

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

- MathematicsSIGA
- 1977

It is shown that the degree-bounds of the directed Hamiltonian circuit with node-degree bounded by 3-out, 1-in or 1- out, 3-in is NP-complete by the following construction~ Expand each node by.

### Node-and edge-deletion NP-complete problems

- Mathematics, Computer ScienceSTOC
- 1978

This paper shows that if &pgr; belongs to a rather broad class of properties then the node-deletion problem is NP-complete, and the same is true for several restrictions of it.

### MSOL Restricted Contractibility to Planar Graphs

- MathematicsIPEC
- 2012

An FPT algorithm is given in time O ( n 2 f ( k ) ) which solves P- RestrictedContract and can solve the l-subgraph contractibility problem in which the edges of the set S are required to form disjoint connected subgraphs of size at most l.

### Planar Graphs and Partial k-Trees

- Mathematics, Computer Science
- 2005

It is proved that any Hamiltonian planar graph on n vertices can be decomposed into a forest and a graph of O(log n) treewidth, and provided an efficient algorithm for constructing this decomposition.

### Circuit Complexity of Properties of Graphs with Constant Planar Cutwidth

- MathematicsMFCS
- 2014

It is shown that for 2-coloring, for bipartite perfect matching, and for several variants of disjoint paths, the straightforward NC 1 upper bound may be improved to AC 0[2], ACC 0, and AC 0 respectively for bounded planar cutwidth graphs.

### NP-Completeness of Max-Cut for Segment Intersection Graphs

- Mathematics
- 2018

We consider the problem of finding a maximum cut in a graph G = (V,E), that is, a partition V1∪̇V2 of V such that the number of edges between V1 and V2 is maximum. It is well known that the decision…

### The Complexity of some Problems Related to Graph 3-colorability

- Mathematics, Computer ScienceDiscret. Appl. Math.
- 1998

### On the hardness of approximating N P witnesses

- Computer ScienceAPPROX
- 2000

It is shown that for many of the well known NP-complete problems it is NP-hard to produce a solution whose Hamming distance from an optimal solution is substantially closer than what one would obtain by just taking a random solution.

### Fair Edge Deletion Problems on Tree-Decomposable Graphs and Improper Colorings ?

- Mathematics, Computer Science
- 2010

Every problem expressible in MSOL is solvable in polynomial time with the fair objective function, on graphs with bounded tree-width, and a Θ( √ n)-approximation algorithm is described.

### On the Complexity of Approximating Colored-Graph Problems

- Computer Science, MathematicsCOCOON
- 1999

This paper proves explicit lower bounds on the approximability of some graph problems restricted to instances which are already colored with a constant number of colors and proposes a generalization of the analysis of the complexity of approximating colored-graph problems to the complexityof approximating approximated optimization problems.

## References

SHOWING 1-10 OF 17 REFERENCES

### Approximation algorithms for combinatorial problems

- Computer Science, MathematicsSTOC
- 1973

For the problem of finding the maximum clique in a graph, no algorithm has been found for which the ratio does not grow at least as fast as 0(nε), where n is the problem size and ε> 0 depends on the algorithm.

### Planar 3-colorability is polynomial complete

- MathematicsSIGA
- 1973

The general problem of recognizing the set of pairs (G,k), where k is a positive integer and G is a graph which is k-colorable, is polynomial complete as defined by Karp [I]. It is shown here that…

### Algorithms for Minimum Coloring, Maximum Clique, Minimum Covering by Cliques, and Maximum Independent Set of a Chordal Graph

- MathematicsSIAM J. Comput.
- 1972

This paper presents ways for constructing efficient algorithms for finding a minimum coloring, a minimum covering by cliques, a maximum clique, and a maximum independent set given a chordal graph.

### Permutation Graphs and Transitive Graphs

- MathematicsJACM
- 1972

Algorithms for finding a maximum size clique and a minimum coloration of transitive grapl are presented and are applicable in solving problems in memo] allocation and circuit layout.

### Optimal linear-ordering.

- Computer Science
- 1973

If G is a rooted tree, an algorithm is presented which requires $O( {n\log n} )$ operations, which establishes a lower bound on the total wire length.

### The complexity of theorem-proving procedures

- Mathematics, Computer ScienceSTOC
- 1971

It is shown that any recognition problem solved by a polynomial time-bounded nondeterministic Turing machine can be “reduced” to the problem of determining whether a given propositional formula is a…

### Reducibility Among Combinatorial Problems

- Computer Science50 Years of Integer Programming
- 1972

Throughout the 1960s I worked on combinatorial optimization problems including logic circuit design with Paul Roth and assembly line balancing and the traveling salesman problem with Mike Held, which made me aware of the importance of distinction between polynomial-time and superpolynomial-time solvability.

### Polynomial complete scheduling problems

- BusinessSOSP '73
- 1973

It is shown that the problem of finding an optimal schedule for a set of jobs is polynomial complete even in the following two restricted cases, tantamount to showing that the scheduling problems mentioned are intractable.

### Algorithms for a maximum clique and a maximum independent set of a circle graph

- MathematicsNetworks
- 1973

Efficient algorithms for finding a maximum clique and a maximum independent set of circle graphs that require at most n3 steps, where n is the number of vertices in the graph.