Counting almost minimum cutsets with reliability applications
Mathematical Programming: Series A and B
A new approach to the maximum-flow problem
Journal of the ACM (JACM)
Computing edge-connectivity in multigraphs and capacitated graphs
SIAM Journal on Discrete Mathematics
A polynomial algorithm for the k-cut problem for fixed k
Mathematics of Operations Research
The Complexity of Multiterminal Cuts
SIAM Journal on Computing
Global min-cuts in RNC, and other ramifications of a simple min-out algorithm
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
Node-and edge-deletion NP-complete problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
A polynomial algorithm for the MIN CUT linear arrangement of trees
SFCS '83 Proceedings of the 24th Annual Symposium on Foundations of Computer Science
Weakly bipartite graphs and the Max-cut problem
Operations Research Letters
On some weakly bipartite graphs
Operations Research Letters
The max-cut problem on graphs not contractible to K5
Operations Research Letters
| Hi-index | 0.98 |
We survey well known problems from statistical mechanics involving optimal cuts of graphs. These problems include finding the ground states for the spin glass problem or for the random field Ising model, as well as finding the lowest energy barrier between the two ground states of a ferromagnet. The relations between the results in graph theory and in physics are outlined. In particular, the solvability of a special max cut problem which arises in statistical mechanics is an easy consequence of a gauge invariance. Throughout the paper, we review some useful algorithms and results. We also give a simple solution of the cutwidth problem in the case of a regular tree.