Note on a min‐max conjecture of Woodall

In 1978 Woodall [ 6 ] conjectured the following: in a planar digraph the size of a shortest cycle is equal to the maximum cardinality of a collection of disjoint tranversals of cycles. We prove that this conjecture is true when the digraph is series‐parallel. In fact, we prove a stronger weighted version that gives the latter result as a corollary. © 2001 John Wiley & Sons, Inc. J Graph Theory 38: 36–41, 2001     

Packing triangles in low degree graphs and indifference graphs

We consider the problems of finding the maximum number of vertex-disjoint triangles (VTP) and edge-disjoint triangles (ETP) in a simple graph. Both problems are NP-hard. The algorithm with the best approximation ratio known so far for these problems has ratio 3/2+?, a result that follows from a more general algorithm for set packing obtained by Hurkens and Schrijver [On the size of systems of sets every t of which have an SDR, with an application to the worst-case ratio of heuristics for packing problems, SIAM J. Discrete Math. 2(1) (1989) 68-72]. We present improvements on the approximation ratio for restricted cases of VTP and ETP that are known to be APX-hard: we give an approximation algorithm for VTP on graphs with maximum degree 4 with ratio slightly less than 1.2, and for ETP on graphs with maximum degree 5 with ratio 4/3. We also present an exact linear-time algorithm for VTP on the class of indifference graphs.     

Persistence of pierisin-1 activities in the adult cabbage white butterfly,Pieris rapae,during storage after killing

Crude extracts from larvae, pupae and adults of cabbage white butterflies, Pieris rapae and Pieris brassicae, and green-veined butterfly, Pieris napi, have an ability to induce apoptosis in the human cancer cell lines. As apoptosis inducing protein, pierisin-1 and -2 have been isolated from pupae of P. rapae and P. brassicae, respectively, and shown to exhibit DNA ADP-ribosylating activity. Although the highest activity was detected in the late phase of larvae and early phase of pupae, certain activity was found in adult butterflies. In order to investigate distribution of substances having pierisin-like activities in butterflies, many species need to be analyzed. However, fresh samples of larvae and pupae are hard to obtain, especially if samples are of scarce species or from overseas. The usage of adult butterflies is practical to examine the distribution of pierisin-like activity in many species. In this study, we examined the cytotoxicity of crude extracts from adults of P. rapae against HeLa cells and DNA ADP-ribosylation ability during storage for 1, 2 and 8 weeks at room temperature after killing adult butterflies after eclosion. Body weights decreased to 18% for 8 weeks through dehydration. Cytotoxicity of samples from butterfly kept for 1, 2 and 8 weeks decreased to 47, 39 and 22%, respectively, of the control value. DNA ADP-ribosylating activity of the samples also decreased to 30, 27 and 23%. Similar reduction was observed on western blot analysis with anti-pierisin-1 antibody. Fortunately, these results suggest that cytotoxic and DNA ADP-ribosylating activity persists to some extent in the body after killing, at least for 8 weeks. Thus, butterfly adult samples kept for two months at room temperature can still be useful for examination of the presence of substance having pierisin-like activity.     

Direct observation of antiferroquadrupolar ordering: resonant X-Ray scattering study of DyB2C2

Antiferroquadrupolar (AFQ) ordering has been conjectured in several rare-earth compounds to explain their anomalous magnetic properties. No direct evidence for AFQ ordering, however, has been reported. Using the resonant x-ray scattering technique near the Dy L(III) absorption edge, we have succeeded in observing the AFQ order parameter in DyB2C2 and analyzing the energy and polarization dependence. The much weaker coupling between the orbital degrees of freedom and the lattice in 4f electron systems than in 3d compounds makes them an ideal platform to study orbital interactions originating from electronic mechanisms.     

Phonon anomalies and superconductivity in the hcp metals,Tc, Re,and Ru

The phonon dispersion curves have been measured for the hcp metals, Tc, Re, and Ru in the [001] direction at room temperature. A pronounced phonon anomaly has been observed for the LO mode in Tc and Re which is absent in Ru. A low temperature study of Tc revealed a strong temperature dependence of the anomaly. It is suggested that the magnitude of the phonon anomaly is correlated with the strength of the electron-phonon interaction in these metals.