## Abstract We show that the following problem is __NP__ complete: Let __G__ be a cubic bipartite graph and __f__ be a precoloring of a subset of edges of __G__ using at most three colors. Can __f__ be extended to a proper edge 3βcoloring of the entire graph __G__? This result provides a natural co
Extremal problems concerning transformations of the edges of the complete hypergraphs
β Scribed by Yair Caro
- Publisher
- John Wiley and Sons
- Year
- 1987
- Tongue
- English
- Weight
- 456 KB
- Volume
- 11
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
β¦ Synopsis
We consider extremal problems concerning transformations of the edges of complete hypergraphs. We estimate the order of the largest subhypergraph K such that for every edge e E β¬(K), f(e) e f ( K ) , assuming f(e) # e. Several extensions and variations of this problem are also discussed here.
π SIMILAR VOLUMES
A colouring of the vertices of a hypergraph G is called strong if, for every edge A, the colours of all vertices in A are distinct. It corresponds to a colouring of the generated graph (G) obtained from G by replacing every edge by a clique. We estimate the minimum number of edges possible in a k-cr
We consider the semilinear elliptic problem where \* is a nonnegative parameter and g is a positive, nondecreasing, convex nonlinearity. There exists a value \*\* of the parameter which is extremal in terms of existence of solution. We study the linearization of the semilinear problem at the extrem
## Abstract Existence of some generalized edge colorings is proved by using the properties of hypergraphs as well as alternating chain methods. A general framework is given for edge colorings and some general properties of balancing are derived.
concerning the well-known diophantine problem of Frobenius was given an exact solution for linear forms with the set of coefficients of density 1 2 (or more). In the present paper, we advance this up to the density 1 3 .
## NOTE T 'OI,. 1 (1967) \* This work was aided by grants-in-aid from t~he USPHG and the Research The two points a t which moral issues arise in reasonable clinical action are: Conncil of tbe City of New York.