A Density Turán Theorem

2016 ◽  
Vol 85 (2) ◽  
pp. 496-524
Author(s):  
Lothar Narins ◽  
Tuan Tran
Keyword(s):  
Turán Theorem

scholarly journals Turán-type results for intersection graphs of boxes

2021 ◽  
pp. 1-6
Author(s):  
István Tomon ◽  
Dmitriy Zakharov
Keyword(s):  
Short Note ◽  
Intersection Graph ◽  
Intersection Graphs ◽  
Poset Dimension ◽  
Axis Parallel ◽  
Turán Theorem ◽  
Separation Dimension

Abstract In this short note, we prove the following analog of the Kővári–Sós–Turán theorem for intersection graphs of boxes. If G is the intersection graph of n axis-parallel boxes in $${{\mathbb{R}}^d}$$ such that G contains no copy of K t,t , then G has at most ctn( log n)2d+3 edges, where c = c(d)>0 only depends on d. Our proof is based on exploring connections between boxicity, separation dimension and poset dimension. Using this approach, we also show that a construction of Basit, Chernikov, Starchenko, Tao and Tran of K2,2-free incidence graphs of points and rectangles in the plane can be used to disprove a conjecture of Alon, Basavaraju, Chandran, Mathew and Rajendraprasad. We show that there exist graphs of separation dimension 4 having superlinear number of edges.

A Turán Theorem for Extensions Via an Erdős-Ko-Rado Theorem for Lagrangians

COMBINATORICA ◽  
2019 ◽  
Vol 39 (5) ◽  
pp. 1149-1171 ◽  
Author(s):  
Adam Bene Watts ◽  
Sergey Norin ◽  
Liana Yepremyan
Keyword(s):  
Turán Theorem

scholarly journals Extremal Graph for Intersecting Odd Cycles

10.37236/5851 ◽  
2016 ◽  
Vol 23 (2) ◽  
Author(s):  
Xinmin Hou ◽  
Yu Qiu ◽  
Boyuan Liu
Keyword(s):  
Complete Graph ◽  
Extremal Graph ◽  
Extremal Graphs ◽  
Turán Theorem ◽  
Odd Cycles ◽  
Turán Graph

An extremal graph for a graph $H$ on $n$ vertices is a graph on $n$ vertices with maximum number of edges that does not contain $H$ as a subgraph. Let $T_{n,r}$ be the Turán graph, which is the complete $r$-partite graph on $n$ vertices with part sizes that differ by at most one. The well-known Turán Theorem states that $T_{n,r}$ is the only extremal graph for complete graph $K_{r+1}$. Erdős et al. (1995) determined the extremal graphs for intersecting triangles and Chen et al. (2003) determined the maximum number of edges of the extremal graphs for intersecting cliques. In this paper, we determine the extremal graphs for intersecting odd cycles.

Necessary and Sufficient Conditions for Mean Convergence of Lagrange Interpolation for Erdős Weights II

1996 ◽  
Vol 48 (4) ◽  
pp. 737-757 ◽  
Author(s):  
S. B. Damelin ◽  
D. S. Lubinsky
Keyword(s):  
Continuous Function ◽  
Lagrange Interpolation ◽  
Sufficient Conditions ◽  
Interpolation Polynomial ◽  
Weighting Factor ◽  
Lagrange Interpolation Polynomial ◽  
Mean Convergence ◽  
Turán Theorem ◽  
Image Position ◽  
Necessary And Sufficient

AbstractWe complete our investigations of mean convergence of Lagrange interpolation at the zeros of orthogonal polynomials pn(W2, x) for Erdős weights W2 = e-2Q. The archetypal example is Wk,α = exp(—Qk,α), whereα > 1, k ≥ 1, and is the k-th iterated exponential. Following is our main result: Let 1 < p < 4 and α ∊ ℝ Let Ln[f] denote the Lagrange interpolation polynomial to ƒ at the zeros of pn(W2, x) = pn(e-2Q, x). Then forto hold for every continuous function ƒ:ℝ. —> ℝ satisfyingit is necessary and sufficient that α > 1/p. This is, essentially, an extension of the Erdös-Turan theorem on L2 convergence. In an earlier paper, we analyzed convergence for all p > 1, showing the necessity and sufficiency of using the weighting factor 1 + Q for all p > 4. Our proofs of convergence are based on converse quadrature sum estimates, that are established using methods of H. König.

Induced Turán Numbers

2017 ◽  
Vol 27 (2) ◽  
pp. 274-288 ◽  
Author(s):  
PO-SHEN LOH ◽  
MICHAEL TAIT ◽  
CRAIG TIMMONS ◽  
RODRIGO M. ZHOU
Keyword(s):  
Upper Bound ◽  
Independent Interest ◽  
Forbidden Subgraphs ◽  
Free Graph ◽  
Induced Subgraph ◽  
Vertex Graph ◽  
Recent Theorem ◽  
Fixed Order ◽  
Turán Theorem ◽  
Asymptotic Upper Bound

The classical Kővári–Sós–Turán theorem states that ifGis ann-vertex graph with no copy ofKs,tas a subgraph, then the number of edges inGis at mostO(n2−1/s). We prove that if one forbidsKs,tas aninducedsubgraph, and also forbidsanyfixed graphHas a (not necessarily induced) subgraph, the same asymptotic upper bound still holds, with different constant factors. This introduces a non-trivial angle from which to generalize Turán theory to induced forbidden subgraphs, which this paper explores. Along the way, we derive a non-trivial upper bound on the number of cliques of fixed order in aKr-free graph with no induced copy ofKs,t. This result is an induced analogue of a recent theorem of Alon and Shikhelman and is of independent interest.

A Generalization of the Turán Theorem and Its Applications

2004 ◽  
Vol 47 (4) ◽  
pp. 573-588 ◽  
Author(s):  
Yu-Ru Liu
Keyword(s):  
Finite Field ◽  
Function Fields ◽  
Number Fields ◽  
General Context ◽  
Turán Theorem

AbstractWe axiomatize the main properties of the classical Turán Theorem in order to apply it to a general context. We provide applications in the cases of number fields, function fields, and geometrically irreducible varieties over a finite field.

scholarly journals ROOTS OF TRIGONOMETRIC POLYNOMIALS AND THE ERDŐS–TURÁN THEOREM

Mathematika ◽  
2020 ◽  
Vol 66 (2) ◽  
pp. 245-254
Author(s):  
Stefan Steinerberger
Keyword(s):  
Trigonometric Polynomials ◽  
Turán Theorem

The number of maximal cliques and spectral radius of graphs with certain forbidden subgraphs

2018 ◽  
Vol 10 (06) ◽  
pp. 1850071
Author(s):  
Ya-Lei Jin ◽  
Xiao-Dong Zhang
Keyword(s):  
Spectral Radius ◽  
Forbidden Subgraphs ◽  
Unique Graph ◽  
Turán Theorem ◽  
Turán Graph

Turán theorem states that the Turán graph [Formula: see text] is the unique graph which has the maximum edge number among the [Formula: see text]-free graphs of order [Formula: see text]. In this paper, we prove that [Formula: see text] has both the maximum number of maximal cliques and the maximum spectral radius among all graphs of order [Formula: see text] with [Formula: see text] and [Formula: see text], where [Formula: see text] stands for the maximum number of disjoint [Formula: see text]cliques of [Formula: see text].

A Spectral Turán Theorem

2005 ◽  
Vol 14 (5-6) ◽  
pp. 755 ◽  
Author(s):  
FAN CHUNG
Keyword(s):  
Turán Theorem
Sign in / Sign up

Export Citation Format

Share Document