Spectral Extremal Results with Forbidding Linear Forests

An ' S Extremal Problem in Randomgraphs : Forbidding Odd

Tournament Matrices with Extremal Spectral Properties

For a tournament matrix M of order n, we de ne its walk space, WM , to be SpanfM 1 : j = 0; . . . ; n 1g where 1 is the all ones vector. We show that the dimension of WM equals the number of eigenvalues of M whose real parts are greater than 1=2. We then focus on tournament matrices whose walk space has particularly simple structure, and characterize them in terms of their spectra. Speci cally,...

Results and Problems on Saturation Numbers for Linear Forests

A graph G is called H-saturated if G contains no copy of H, but for any edge e in the complement of G, the graph G + e contains some copy of H. The minimum size of an n-vertex H-saturated graph is denoted by sat(n,H) and is called the saturation number of H. In [?], Kászonyi and Tuza determined the values of sat(n,H) when H is a path or a disjoint union of edges. In this paper, we determine the...

Spectral Extremal Problems for Hypergraphs

In this paper we consider spectral extremal problems for hypergraphs. We give two general criteria under which such results may be deduced from ‘strong stability’ forms of the corresponding (pure) extremal results. These results hold for the α-spectral radius defined using the α-norm for any α > 1; the usual spectral radius is the case α = 2. Our results imply that any hypergraph Turán problem ...

New results in extremal problems with polynomials

In this paper we give some new results in extremal problems with polynomials which are generalization of some results of F. Locher. 2000 Mathematical Subject Classification: 26D15, 65D32 In [6] F. Locher studies some extremal problems for semidefinition polynomials (nenegative or nepositive) with the dominant coefficient equal to 1. For this he uses the quadrature formulae with high algebraical...