Four fundamental graph problems, Minimum vertex cover, Maximum independent set, Minimum dominating set and Maximum cut, are shown to be APX-complete even for cubic graphs. Therefore, unless P = NP, these problems do not admit any polynomial time approximation scheme on input graphs of degree bounded
Some arrowing results for trees versus complete graphs
β Scribed by Albert D. Polimeni; H. JosephS Straight; Jay Yellen
- Book ID
- 118284384
- Publisher
- John Wiley and Sons
- Year
- 1981
- Tongue
- English
- Weight
- 288 KB
- Volume
- 5
- Category
- Article
- ISSN
- 0364-9024
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## Abstract We investigate tree decompositions (__T__,(__X__~t~)~tΟ΅V(T)~) whose width is βclose to optimalβ and such that all the subtrees of __T__ induced by the vertices of the graph are βsmall.β We prove the existence of such decompositions for various interpretations of βclose to optimalβ and β
Shee, S.-C., Some results on I-valuation of graphs involving complete bipartite graphs, Discrete Mathematics 87 (1991) 73-80. In this paper we show that a graph G obtained from a complete bipartite graph K,,, and a collection of q (cmax{m, n}) stars G, by joining the centre of G, to every vertex of