The splittance of an arbitrary graph is the minimum number of edges to be added or removed in order to produce a split graph (i.e. a graph whose vertex set can be partitioned into a clique and an independent set). The splittance is seen to depend only on the degree sequence of the graph, and an explicit formula for it is derived. This result allows to give a simple characterization of the degree sequences of split graphs. Worst cases for the splittance are determined for some classes of graphs (the class of all graphs, of all trees and of all planar graphs).
AMS subject classification (1980)05 C 35
Unable to display preview. Download preview PDF.
- A. Bondy andU. S. R. Murty,Graph Theory with Applications, MacMillan, London, 1976.Google Scholar
- P. Erdős andT. Gallai, Graphen mit Punkten vorgeschriebenen Grades,Mat. Lapok,11 (1960), 264–274.Google Scholar
- S. Földes andP. L. Hammer, On a class of matroid producing graphs,Coll. Math. Soc. J. Bolyai, Combinatorics, Budapest,18 (1978), 331–352.Google Scholar
- S. Földes andP. L. Hammer, Split graphs,Proceedings of the 8th South-Eastern Conference on Combinatorics, Graph Theory and Computing, (1977), 311–315.Google Scholar
- M. R. Garey, D. S. Johnson andL. Stockmeyer, Some simplified NP-complete Problems,Proc. 6th ACM Symp. on Theory of Computing, Seattle (1974).Google Scholar
- H. J. Ryser,Combinatorial Mathematics, Carus Monographs, American Mathematical Society (1963).Google Scholar