منابع مشابه
Splitting Number is NP-complete
We consider two graph invariants that are used as a measure of nonplanarity: the splitting number of a graph and the size of a maximum planar subgraph. The splitting number of a graph G is the smallest integer k 0, such that a planar graph can be obtained from G by k splitting operations. Such operation replaces a vertex v by two nonadjacent vertices v1 and v2, and attaches the neighbors of v e...
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We propose an algorithm for finding zero divisors in quaternion algebras over quadratic number fields, or equivalently, solving homogeneous quadratic equations in three variables over Q( √ d) where d is a square-free integer. The algorithm is deterministic and runs in polynomial time if one is allowed to call oracles for factoring integers and polynomials over finite fields.
متن کاملSplitting Number and the Core Model
We provide a lower bound for the consistency strength of the hypothesis proposed by S. Kamo: ∃κ > א0 s(κ) ≥ κ. 0. Introduction. In [3] ,[10] cardinal invariants on ω are generalized for uncountable regular cardinals and it is shown that some of their properties still hold true for their uncountable counterparts.However,the role of the splitting number s(κ) (for the definition see below) changes...
متن کاملThe Splitting Number of the 4-Cube
The splitting number of a graph G consists in the smallest positive integer k 0, such that a planar graph can be obtained from G by k splitting operations, such operation replaces v by two nonadjacent vertices v1 and v2, and attaches the neighbors of v either to v1 or to v2. One of the most useful graphs in computer science is the n{cube. Dean and Richter devoted an article to proving that the ...
متن کاملOn the splitting number at Regular Cardinals
Let κ, λ be regular uncountable cardinals such that λ > κ+ is not a successor of a singular cardinal of low cofinality. We construct a generic extension with s(κ) = λ starting from a ground model in which o(κ) = λ and prove that assuming ¬0¶, s(κ) = λ implies that o(κ) ≥ λ in the core model.
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1997
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-97-03758-1