Delorme, C. and S. Poljak, The performance of an eigenvalue bound on the max-cut problem in some classes of graphs, Discrete Mathematics 111 (1993) 145-156. The authors earlier introduced a number q(C), which gives a well-computable upper bound on the maximum bipartite subgraph of a graph or, more
The max clique problem in classes of string-graphs
β Scribed by M. Middendorf; F. Pfeiffer
- Publisher
- Elsevier Science
- Year
- 1992
- Tongue
- English
- Weight
- 378 KB
- Volume
- 108
- Category
- Article
- ISSN
- 0012-365X
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β¦ Synopsis
Middendorf, M., F. Pfeiffer, The max clique problem in classes of string-graphs, Discrete Mathematics 108 (1992) 365-372. A string-graph is an intersection graph of a set of curves in the plane. Investigating the complexity of the max clique problem for some classes of string-graphs we obtain NPcompleteness results on one hand and polynomial time algorithms on the other hand for string-graph-classes of at first sight surprising similarity.
π SIMILAR VOLUMES
Denote the number of vertices of G by ]G[. A clique of graph G is a maximal complete subgraph. The density oJ(G) is the number of vertices in the largest clique of G. If Β’o(G)>~Β½ ]GI, then G has at most 2 tΒ°l-'cG) cliques. The extremal graphs are then examined as wen. ## Terminology We will be co
## Abstract The MatchingβCut problem is the problem to decide whether a graph has an edge cut that is also a matching. Previously this problem was studied under the name of the Decomposable Graph Recognition problem, and proved to be ${\cal{NP}}$βcomplete when restricted to graphs with maximum deg