## Abstract We consider the family of graphs with a fixed number of vertices and edges. Among all these graphs, we are looking for those minimizing the sum of the square roots of the vertex degrees. We prove that there is a unique such graph, which consists of the largest possible complete subgraph
On the regularization of a class of unstable extremal problems
β Scribed by M.G. Dmitriev; V.S. Poleshchuk
- Publisher
- Elsevier Science
- Year
- 1972
- Weight
- 221 KB
- Volume
- 12
- Category
- Article
- ISSN
- 0041-5553
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π SIMILAR VOLUMES
## Abstract A (plane) 4βregular map __G__ is called __C__βsimple if it arises as a superposition of simple closed curves (tangencies are not allowed); in this case Ο (__G__) is the smallest integer __k__ such that the curves of __G__ can be colored with __k__ colors in such a way that no two curves
Existence of a unique solution for a class of regular singular two point boundary value problems . and with quite general conditions on f x, y . These conditions on f x, y are sharp, which is seen through one example. Regions for multiple solutions have also been determined.