Spectral Saturation: Inverting the Spectral Turán Theorem
نویسندگان
چکیده
منابع مشابه
Spectral Saturation: Inverting the Spectral Turán Theorem
Let μ (G) be the largest eigenvalue of a graph G and Tr (n) be the r-partite Turán graph of order n. We prove that if G is a graph of order n with μ (G) > μ (Tr (n)) , then G contains various large supergraphs of the complete graph of order r + 1, e.g., the complete r-partite graph with all parts of size log n with an edge added to the first part. We also give corresponding stability results.
متن کاملA note on spectral mapping theorem
This paper aims to present the well-known spectral mapping theorem for multi-variable functions.
متن کاملThe Spectral Theorem and Beyond
We here present the main conclusions and theorems from a first rigorous inquiry into linear algebra. Although some basic definitions and lemmas have been omitted so to keep this exposition decently short, all the main theorems necesary to prove and understand the spectral, or diagonalization, theorem are here presented. A special attention has been placed on making the proofs not only proofs of...
متن کاملCommutative Spectral Triples & The Spectral Reconstruction Theorem A Master
Given a unital and commutative algebra A associated to a spectral triple, we show how a differentiable structure is constructed on the spectrum of such an algebra whenever the spectral triple satisfies eight so-called “axioms”, in such a way that A ∼= C∞(M). This construction is the celebrated “reconstruction theorem” of Alain Connes [14], [21]. We discuss two spin manifolds, the circle and the...
متن کاملA Computable Spectral Theorem
Computing the spectral decomposition of a normal matrix is among the most frequent tasks to numerical mathematics. A vast range of methods are employed to do so, but all of them suffer from instabilities when applied to degenerate matrices, i.e., those having multiple eigenvalues. We investigate the spectral representation’s effectivity properties on the sound formal basis of computable analysi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2009
ISSN: 1077-8926
DOI: 10.37236/122