Let ex(n,C4) denote the maximum size of a C4-free graph of order n. For an even integer or odd prime power q > 6, we prove that ex(q2 + q + 2, C4) < 1 2(q+1)(q 2+q+2), which leads to an improvement of the upper bounds on Ramsey numbers R(C4,Wq2+2), where Wn is a wheel of order n. By using a simple polarity graph Gq for a prime power q, we construct the graphs whose complements do not contain K1...

An edge e of a simple 3-connected graph G is essential if neither the deletion G\e nor the contraction G/e is both simple and 3–connected. Tutte’s Wheels Theorem proves that the only simple 3–connected graphs with no non-essential edges are the wheels. In earlier work, as a corollary of a matroid result, the authors determined all simple 3-connected graphs with at most two non-essential edges. ...

In maturing rats, the growth of abdominal fat is attenuated by voluntary wheel running. After the cessation of running by wheel locking, a rapid increase in adipose tissue growth to a size that is similar to rats that have never run (i.e. catch-up growth) has been previously reported by our lab. In contrast, diet-induced increases in adiposity have a slower onset with relatively delayed transcr...

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Tutte’s Wheels-and-Whirls Theorem proves that if M is a 3-connected matroid other than a wheel or a whirl, then M has a 3-connected minor N such that |E(M)| − |E(N)| = 1. Geelen and Whittle extended this theorem by showing that when M is sequentially 4-connected, the minor N can also be guaranteed to be sequentially 4connected, that is, for every 3-separation (X, Y ) of N , the set E(N) can be ...

An essential element of a 3–connected matroid M is one for which neither the deletion nor the contraction is 3–connected. Tutte’s Wheels and Whirls Theorem proves that the only 3–connected matroids in which every element is essential are the wheels and whirls. In an earlier paper, the authors showed that a 3–connected matroid with at least one non-essential element has at least two such element...

In front wheels driven vehicles, fuel economy can be obtained by summing torques applied to rear wheels. On the other hand, unequal torques applied to rear wheels provides enhanced safety. In this paper, a model with seven degrees of freedom is considered for the vehicle body. Thereafter, power-train subsystems are modeled. Considering an electrical machine on each rear wheel, a fuzzy controlle...

in this work, time domain analysis is used to solve adler’s equation in order to obtain the required time, for an oscillator under external injection, reaching the steady-state condition. mathematical approach has been applied to fully describe the transient of frequency acquisition in injection-locked lc and ring oscillators considering their time-varying nature. then, the analysis is verified...

Wheel slip activity detection is crucial in railway maintenance, as it can contribute to avoiding wheel damage but also track deteriorations leading significant maintenance costs, trains delays, well the risk of accidents. characterised by lower adhesion between and wheel, especially braking conditions, locking wheels. It complex model or predict, being influenced a multitude factors including ...