Digital image processing (2nd ed.)
Digital image processing (2nd ed.)
Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
A linear algorithm for bipartition of biconnected graphs
Information Processing Letters
A recursive characterization of the 4-connected graphs
Discrete Mathematics
On-line maintenance of the four-components of a graph (extended abstract)
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Approximating the maximally balanced connected partition problem in graphs
Information Processing Letters
Efficient Algorithms for Tripartitioning Triconnected Graphs and 3-Edge-Connected Graphs
WG '93 Proceedings of the 19th International Workshop on Graph-Theoretic Concepts in Computer Science
Convex Embeddings and Bisections of 3-Connected Graphs1
Combinatorica
Operating systems
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Let G=(V,E) be an undirected graph with a node set V and an arc set E. G has k pairwise disjoint subsets T"1,T"2,...,T"k of nodes, called resource sets, where |T"i| is even for each i. The partition problem with k resource sets asks to find a partition V"1 and V"2 of the node set V such that the graphs induced by V"1 and V"2 are both connected and |V"1@?T"i|=|V"2@?T"i|=|T"i|/2 holds for each i=1,2,...,k. The problem of testing whether such a bisection exists is known to be NP-hard even in the case of k=1. On the other hand, it is known that if G is (k+1)-connected for k=1,2, then a bisection exists for any given resource sets, and it has been conjectured that for k=3, a (k+1)-connected graph admits a bisection. In this paper, we show that for k=3, the conjecture does not hold, while if G is 4-connected and has K"4 as its subgraph, then a bisection exists and it can be found in O(|V|^3log|V|) time. Moreover, we show that for an arc-version of the problem, the (k+1)-edge-connectivity suffices for k=1,2,3.