C6-free bipartite graphs and product representation of squares

Győri, Ervin

doi:10.1016/s0012-365x(96)00184-7

Cited by 41 publications

(58 citation statements)

References 2 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For instance, for k=3 we show that π(n)+π(n/2)+cn 2/3 (log n) 4/3 ≤ G 3 (n)≤π(n)+π(n/2)+cn 2/3 (log n)/(loglog n), and for k=4 π(n)+n 3/5 / (log n) 6/5 ≤G 4 (n)≤π(n)+cn 2/3 (where π(x) denotes the number of primes up to x). These results strengthen some results of Erdős, Sárközy, T. Sós [137] and Győri [139] concerning a strongly related problem from combinatorial number theory: How many elements of the set {1, 2, ..., n} can be chosen in such a way that none of the 2k-factor products from this set is a perfect square?…”

Section: Further Combinatorial Resultssupporting

confidence: 84%

BME VIK Annual Research Report on Electrical Engineering and Computer Science 2015

Vajk¹,

Harsányi

Poppe

et al. 2016

Period. Polytech. Elec. Eng. Comp. Sci.

View full text Add to dashboard Cite

PrefaceThroughout László Vajta, Dean of BME VIK János Levendovszky, Deputy Dean of BME VIK Department of Automation and Applied InformaticsDepartment of Automation and Applied Informatics (AUT) is one of the largest and dynamically developing departments at BME with diverse scope competences such as control theory, embedded systems, software modelling, applied software development, Internet of Things, power electronics, mechatronics, and many others. The department's main activities are education, research and development. Training versatile electrical and software engineers with solid practical knowledge is our top priority. Our profile also includes developing high quality software and hardware solutions for industry partners. All of our activities are backed by strong research background.In 2015, the department has organized the 21 st European Wireless (EW) Conference. The EW 2015 conference hosted more than 140 participants from 30 different countries. The 2015 edition of EW was aimed at addressing a key theme on "5G and beyond."The next sections summarize the key research results of the department in year 2015. IoT and Smart CityThe Internet of Things (IoT) is transforming the surrounding physical objects into an ecosystem of information that enriches our everyday life. The IoT represents the convergence of advances in miniaturization, wireless connectivity, and increased data storage, and is driven by various sensors. Application and service development methods and frameworks are required to support the realization of solutions covering data collection, transmission, data processing, analysis, reporting, and advanced querying. Our SensorHUB framework URBMOBI is a mobile environmental sensor that (i) provides temporally and spatially distributed environmental data, (ii) fulfills the need for monitoring at various places without the costs for a large number of fixed measurement stations, (iii) integrates small and precise sensors in a system that can be operated on buses, trams, or other vehicles, (iv) concentrates on urban heat and thermal comfort, and (v) aims at providing climate services and integration with real-time climate models.utilizes the state-of-the-art open source technologies and provides a unified tool chain for IoT related application and ser-URBMOBI project has been worked out between 2013 and 2015 by the following consortium: RWTH Aachen University (Germany), Netherlands Organization for Applied Scientific Research TNO (Netherlands), ARIA Technologies (France), Budapest University of Technology and Economics (Hungary), and Meteorological and Environmental Earth Observation (Italy).The SOLSUN (Sustainable Outdoor Lighting & Sensory Urban Networks) project is about to demonstrate how intelligent city infrastructure can be created in a cost-effective and sustainable way by reusing existing street lighting as the communications backbone. We apply different technologies and methods to reduce energy consumption at the same time as turning streetlights into nodes on a scalable network that is al...

show abstract

Section: Further Combinatorial Resultssupporting

confidence: 84%

BME VIK Annual Research Report on Electrical Engineering and Computer Science 2015

Vajk¹,

Harsányi

Poppe

et al. 2016

Period. Polytech. Elec. Eng. Comp. Sci.

View full text Add to dashboard Cite

show abstract

“…There is a number of results of this type, see, e.g., Győri [5]. Also the sizes grow exponentially, one can easily generalize it for other sequences.…”

Section: Union-free Subfamiliesmentioning

confidence: 88%

Large $B_d$-Free and Union-free Subfamilies

Barát¹,

Füredi²,

Kantor³

et al. 2012

SIAM J. Discrete Math.

View full text Add to dashboard Cite

show abstract

“…Theorem (Győri, [7]). There exists such a constant c > 0 that the following inequality holds: F 6 (n) ≤ π(n) + π(n/2) + cn 2/3 log n.…”

Section: Corollariesmentioning

confidence: 99%

“…Erdős, Sárközy and T. Sós proved the following estimates for k = 3: π(n) + π (n/2) + c n 2/3 (log n) 4/3 ≤ F 6 (n) ≤ π(n) + π (n/2) + cn 7/9 log n. Besides, they noted that by improving their graph theoretic lemma used in the proof the upper bound π(n) + π(n/2) + cn 2/3 log n could be obtained, so the lower and upper bounds would only differ in a logpower factor in the error term. Later Győri [7] improved this graph theoretic lemma, and gained the desired bound. Furthermore, Erdős, Sárközy and T. Sós gave the following estimates for k = 4:…”

Section: Introductionmentioning

confidence: 99%