A note on dominating cycles in 2-connected graphs

Let G be a 2-connected graph on n vertices such that d(x) + d(y) + d(z) n for all triples of independent vertices x, y, z. We prove that every longest cycle in G is a dominating cycle unless G is a spanning subgraph of a graph belonging to one of four easily specified classes of graphs

Zero-field Quantum Critical Point in CeCoIn5_5

Quantum criticality in the normal and superconducting state of the heavy-fermion metal CeCoIn$_5$ is studied by measurements of the magnetic Gr\"{u}neisen ratio, $\Gamma_H$, and specific heat in different field orientations and temperatures down to 50 mK. Universal temperature over magnetic field scaling of $\Gamma_H$ in the normal state indicates a hidden quantum critical point at zero field. Within the superconducting state the quasiparticle entropy at constant temperature increases upon reducing the field towards zero, providing additional evidence for zero-field quantum criticality.Comment: submitted to PR

Polynomial algorithms that prove an NP-hard hypothesis implies an NP-hard conclusion

A number of results in Hamiltonian graph theory are of the form $\mathcal{P}$$_{1}$ implies $\mathcal{P}$$_{2}$, where $\mathcal{P}$$_{1}$ is a property of graphs that is NP-hard and $\mathcal{P}$$_{2}$ is a cycle structure property of graphs that is also NP-hard. Such a theorem is the well-known Chv\'{a}tal-Erd\"{o}s Theorem, which states that every graph $G$ with $\alpha \leq \kappa$ is Hamiltonian. Here $\kappa$ is the vertex connectivity of $G$ and $\alpha$ is the cardinality of a largest set of independent vertices of $G$. In another paper Chv\'{a}tal points out that the proof of this result is in fact a polynomial time construction that either produces a Hamilton cycle or a set of more than $\kappa$ independent vertices. In this note we point out that other theorems in Hamiltonian graph theory have a similar character. In particular, we present a constructive proof of the well-known theorem of Jung for graphs on $16$ or more vertices.. \u

Quality Assessment of Summer and Autumn Carrots from a Biodynamic Breeding Project and Correlations of Physico-Chemical Parameters and Features Determined by Picture Forming Methods

Introduction: Assessment of product quality is of special significance in organic farming and includes the supervision of crop quality in different growing systems (e.g., Fleck et al. 1998) and the characterisation of different cultivars. Several methods have been developed and applied for this purpose, e.g., the physico-chemical analysis of crops, picture forming methods (PFMs) and plant observation. So far only limited information is available on the comparability of these methods. This contribution aims to compare the results of the analysis of physico-chemical parameters of summer and autumn carrots with features determined by PFMs by means of correlation analysis. Conclusions: High and significant correlation coefficients were found between quality parameters of summer and autumn carrots from a biodynamical breeding project determined by physico-chemical analysis and PFMs. This indicates close relationships between the two quality approaches which should be investigated further in future work

Large magnetoresistance in the antiferromagnetic semi-metal NdSb

There has been considerable interest in topological semi-metals that exhibit extreme magnetoresistance (XMR). These have included materials lacking inversion symmetry such as TaAs, as well Dirac semi-metals such as Cd3As2. However, it was reported recently that LaSb and LaBi also exhibit XMR, even though the rock-salt structure of these materials has inversion symmetry, and the band-structure calculations do not show a Dirac dispersion in the bulk. Here, we present magnetoresistance and specific heat measurements on NdSb, which is isostructural with LaSb. NdSb has an antiferromagnetic groundstate, and in analogy with the lanthanum monopnictides, is expected to be a topologically non-trivial semi-metal. We show that NdSb has an XMR of 10^4 %, even within the AFM state, illustrating that XMR can occur independently of the absence of time reversal symmetry breaking in zero magnetic field. The persistence of XMR in a magnetic system offers promise of new functionality when combining topological matter with electronic correlations. We also find that in an applied magnetic field below the Neel temperature there is a first order transition, consistent with evidence from previous neutron scattering work.Comment: 5 pages, 6 figure