### Abstract

The authors propose a new point of view on graph connectivity that is based on geometric and physical intuition. The main theorem is a geometric characterization of k-vertex connected graphs. It says that a graph G is k-connected if and only if G has a certain 'nondegenerate convex embedding' in R**k- **1 . Probabilistic algorithms for computing the connectivity of a graph are given. The first is a Monte Carlo algorithm that runs in time O(n**2 **. **5 plus nk**2 **. **5 ), where n is the number of vertices and k is the vertex connectivity of the input graph. The second is a Las Vegas algorithm (i. e. , one that never errs) that runs in expected time O(kn**2 **. **5 plus nk**3 **. **5 ).

Original language | English |
---|---|

Title of host publication | Annual Symposium on Foundations of Computer Science (Proceedings) |

Publisher | IEEE |

Pages | 39-48 |

Number of pages | 10 |

ISBN (Print) | 0818607408 |

Publication status | Published - 1986 |

### ASJC Scopus subject areas

- Hardware and Architecture

### Cite this

*Annual Symposium on Foundations of Computer Science (Proceedings)*(pp. 39-48). IEEE.

**PHYSICAL INTERPRETATION OF GRAPH CONNECTIVITY, AND ITS ALGORITHMIC APPLICATIONS.** / Linial, N.; Lovász, L.; Wigderson, A.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Annual Symposium on Foundations of Computer Science (Proceedings).*IEEE, pp. 39-48.

}

TY - GEN

T1 - PHYSICAL INTERPRETATION OF GRAPH CONNECTIVITY, AND ITS ALGORITHMIC APPLICATIONS.

AU - Linial, N.

AU - Lovász, L.

AU - Wigderson, A.

PY - 1986

Y1 - 1986

N2 - The authors propose a new point of view on graph connectivity that is based on geometric and physical intuition. The main theorem is a geometric characterization of k-vertex connected graphs. It says that a graph G is k-connected if and only if G has a certain 'nondegenerate convex embedding' in R**k- **1 . Probabilistic algorithms for computing the connectivity of a graph are given. The first is a Monte Carlo algorithm that runs in time O(n**2 **. **5 plus nk**2 **. **5 ), where n is the number of vertices and k is the vertex connectivity of the input graph. The second is a Las Vegas algorithm (i. e. , one that never errs) that runs in expected time O(kn**2 **. **5 plus nk**3 **. **5 ).

AB - The authors propose a new point of view on graph connectivity that is based on geometric and physical intuition. The main theorem is a geometric characterization of k-vertex connected graphs. It says that a graph G is k-connected if and only if G has a certain 'nondegenerate convex embedding' in R**k- **1 . Probabilistic algorithms for computing the connectivity of a graph are given. The first is a Monte Carlo algorithm that runs in time O(n**2 **. **5 plus nk**2 **. **5 ), where n is the number of vertices and k is the vertex connectivity of the input graph. The second is a Las Vegas algorithm (i. e. , one that never errs) that runs in expected time O(kn**2 **. **5 plus nk**3 **. **5 ).

UR - http://www.scopus.com/inward/record.url?scp=0022882768&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0022882768&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:0022882768

SN - 0818607408

SP - 39

EP - 48

BT - Annual Symposium on Foundations of Computer Science (Proceedings)

PB - IEEE

ER -