共查询到20条相似文献,搜索用时 15 毫秒
1.
We prove Ramsey-type results for intersection graphs of geometric objects. In particular, we prove the following bounds, all
of which are tight apart from the constant c. There is a constant c > 0 such that for every family F of n convex sets in the plane, the intersection graph of F or its complement contains a balanced complete bipartite graph of size at least cn. There is a constant c > 0 such that for every family F of n x-monotone curves in the plane, the intersection graph G of F contains a balanced complete bipartite graph of size at least cn/log n or the complement of G contains a balanced complete bipartite graph of size at least cn. Our bounds rely on new Turán-type results on incomparability graphs of partially ordered sets. 相似文献
2.
Meryam Ben Said Khaled Mehrez Jamel El Kamel 《Journal of Difference Equations and Applications》2018,24(1):48-58
Intrinsic inequalities involving Turán-type inequalities for some q-special functions are established. A special interest is granted to q-Dunkl kernel. The results presented here would provide extensions of those given in the classical case. 相似文献
3.
Jie Han Patrick Morris Guanghui Wang Donglei Yang 《Random Structures and Algorithms》2024,64(1):94-124
For a -vertex graph and an -vertex graph , an -tiling in is a collection of vertex-disjoint copies of in . For , the -independence number of , denoted , is the largest size of a -free set of vertices in . In this article, we discuss Ramsey–Turán-type theorems for tilings where one is interested in minimum degree and independence number conditions (and the interaction between the two) that guarantee the existence of optimal -tilings. Our results unify and generalise previous results of Balogh–Molla–Sharifzadeh [Random Struct. Algoritm. 49 (2016), no. 4, 669–693], Nenadov–Pehova [SIAM J. Discret. Math. 34 (2020), no. 2, 1001–1010] and Balogh–McDowell–Molla–Mycroft [Comb. Probab. Comput. 27 (2018), no. 4, 449–474] on the subject. 相似文献
4.
G. Dirac 《Acta Mathematica Hungarica》1963,14(3-4):417-422
5.
Piyush Kumar Bhandari Sushil Kumar Bissu 《Integral Transforms and Special Functions》2016,27(12):956-964
The aim of this paper is to establish the Turán-type inequalities for Struve functions, modified Struve functions, Anger–Weber functions and Hurwitz zeta function, by using a new form of the Cauchy–Bunyakovsky–Schwarz inequality. 相似文献
6.
Jessica De Silva Kristin Heysse Adam Kapilow Anna Schenfisch Michael Young 《Discrete Mathematics》2018,341(2):492-496
For two graphs and , the Turán number is the maximum number of edges in a subgraph of that contains no copy of . Chen, Li, and Tu determined the Turán numbers for all Chen et al. (2009). In this paper we will determine the Turán numbers for all and . 相似文献
7.
The Turán number is the maximum number of edges in any -vertex graph that does not contain a subgraph isomorphic to . A wheel is a graph on vertices obtained from a by adding one vertex and making adjacent to all vertices of the . We obtain two exact values for small wheels: Given that is already known, this paper completes the spectrum for all wheels up to 7 vertices. In addition, we present the construction which gives us the lower bound in general case. 相似文献
8.
9.
For 0<1 and graphsG andH, we writeGH if any -proportion of the edges ofG span at least one copy ofH inG. As customary, we writeC
k for a cycle of lengthk. We show that, for every fixed integerl1 and real >0, there exists a real constantC=C(l, ), such that almost every random graphG
n, p withp=p(n)Cn
–1+1/2l
satisfiesG
n,p1/2+
C
2l+1. In particular, for any fixedl1 and >0, this result implies the existence of very sparse graphsG withG
1/2+
C
2l+1.The first author was partially supported by NSERC. The second author was partially supported by FAPESP (Proc. 93/0603-1) and by CNPq (Proc. 300334/93-1). The third author was partially sopported by KBN grant 2 1087 91 01. 相似文献
10.
Analysis Mathematica - Let P(x) be an arbitrary algebraic polynomial of degree n with all zeros in the unit interval ?1 ≤ x ≤ 1. We establish the Turán-type inequality... 相似文献
11.
12.
We show that every hypersurface in ? s × ? s contains a large grid, i.e., the set of the form S × T, with S, T ? ? s . We use this to deduce that the known constructions of extremal K 2,2-free and K 3,3-free graphs cannot be generalized to a similar construction of K s,s -free graphs for any s ≥ 4. We also give new constructions of extremal K s,t -free graphs for large t. 相似文献
13.
Harald Niederreiter 《Monatshefte für Mathematik》2010,11(2):193-222
We consider hybrid sequences, that is, sequences in a multidimensional unit cube that are composed from lower-dimensional sequences of two different types. We establish nontrivial deterministic discrepancy bounds for five kinds of hybrid sequences as well as a new version of the Erdös–Turán–Koksma inequality which is suitable for hybrid sequences. 相似文献
14.
15.
Oleg Pikhurko 《Combinatorica》2008,28(2):187-208
Let Σ
k
consist of all k-graphs with three edges D
1, D
2, D
3 such that |D
1 ∩ D
2| = k − 1 and D
1 Δ D
2 ⊆ D
3. The exact value of the Turán function ex(n, Σ
k
) was computed for k = 3 by Bollobás [Discrete Math. 8 (1974), 21–24] and for k = 4 by Sidorenko [Math Notes 41 (1987), 247–259].
Let the k-graph T
k
∈ Σ
k
have edges
Frankl and Füredi [J. Combin. Theory Ser. (A) 52 (1989), 129–147] conjectured that there is n
0 = n
0(k) such that ex(n, T
k
) = ex(n, Σ
k
) for all n ≥ n
0 and had previously proved this for k = 3 in [Combinatorica 3 (1983), 341–349]. Here we settle the case k = 4 of the conjecture.
Reverts to public domain after 28 years from publication.
Partially supported by the National Science Foundation, Grant DMS-0457512. 相似文献
16.
LetH r be anr-uniform hypergraph. Letg=g(n;H r ) be the minimal integer so that anyr-uniform hypergraph onn vertices and more thang edges contains a subgraph isomorphic toH r . Lete =f(n;H r ,εn) denote the minimal integer such that everyr-uniform hypergraph onn vertices with more thane edges and with no independent set ofεn vertices contains a subgraph isomorphic toH r . We show that ifr>2 andH r is e.g. a complete graph then $$\mathop {\lim }\limits_{\varepsilon \to 0} \mathop {\lim }\limits_{n \to \infty } \left( {\begin{array}{*{20}c} n \\ r \\ \end{array} } \right)^{ - 1} f(n;H^r ,\varepsilon n) = \mathop {\lim }\limits_{n \to \infty } \left( {\begin{array}{*{20}c} n \\ r \\ \end{array} } \right)^{ - 1} g(n;H^r )$$ while for someH r with \(\mathop {\lim }\limits_{n \to \infty } \left( {\begin{array}{*{20}c} n \\ r \\ \end{array} } \right)^{ - 1} g(n;H^r ) \ne 0\) $$\mathop {\lim }\limits_{\varepsilon \to 0} \mathop {\lim }\limits_{n \to \infty } \left( {\begin{array}{*{20}c} n \\ r \\ \end{array} } \right)^{ - 1} f(n;H^r ,\varepsilon n) = 0$$ . This is in strong contrast with the situation in caser=2. Some other theorems and many unsolved problems are stated. 相似文献
17.
Some sharp two-sided Turán type inequalities for parabolic cylinder functions and Tricomi confluent hypergeometric functions are deduced. The proofs are based on integral representations for quotients of parabolic cylinder functions and Tricomi confluent hypergeometric functions, which arise in the study of the infinite divisibility of the Fisher–Snedecor F distribution. Moreover, some complete monotonicity results are given concerning Turán determinants of Tricomi confluent hypergeometric functions. These complement and improve some of the results of Ismail and Laforgia (in Constr. Approx. 26:1–9, 2007). 相似文献
18.
19.
Tomasz Dzido 《Graphs and Combinatorics》2013,29(5):1305-1309
The Turán number ex(n, G) is the maximum number of edges in any n-vertex graph that does not contain a subgraph isomorphic to G. We consider a very special case of the Simonovits’s theorem (Simonovits in: Theory of graphs, Academic Press, New York, 1968) which determine an asymptotic result for Turán numbers for graphs with some properties. In the paper we present a more precise result for even wheels. We provide the exact value for Turán number ex(n, W 2k ) for n ≥ 6k ? 10 and k ≥ 3. In addition, we show that ${ex(n,W_6)= \lfloor\frac{n^2}{3}\rfloor}$ for all n ≥ 6. These numbers can be useful to calculate some Ramsey numbers. 相似文献
20.
Árpád Baricz Dragana Jankov Tibor K. Pogány 《Journal of Mathematical Analysis and Applications》2012,388(2):716-724
Complete monotonicity, Laguerre and Turán type inequalities are established for the so-called Krätzel function , defined by where and . Moreover, we prove the complete monotonicity of a determinant function of which entries involve the Krätzel function. 相似文献