Star 5-edge-colorings of subcubic multigraphs

The star chromatic index of a multigraph $G$, denoted $\chi'_{s}(G)$, is the minimum number of colors needed to properly color the edges of $G$ such that no path or cycle of length four is bi-colored. A multigraph $G$ is star $k$-edge-colorable if $\chi'_{s}(G)\le k$. Dvo\v{r}\'ak, Mohar and \v{S}\'amal [Star chromatic index, J Graph Theory 72 (2013), 313--326] proved that every subcubic multigraph is star $7$-edge-colorable, and conjectured that every subcubic multigraph should be star $6$-edge-colorable. Kerdjoudj, Kostochka and Raspaud considered the list version of this problem for simple graphs and proved that every subcubic graph with maximum average degree less than $7/3$ is star list-$5$-edge-colorable. It is known that a graph with maximum average degree $14/5$ is not necessarily star $5$-edge-colorable. In this paper, we prove that every subcubic multigraph with maximum average degree less than $12/5$ is star $5$-edge-colorable.Comment: to appear in Discrete Mathematics. arXiv admin note: text overlap with arXiv:1701.0410

A compilation of known QSOs for the Gaia mission

Quasars are essential for astrometric in the sense that they are spatial stationary because of their large distance from the Sun. The European Space Agency (ESA) space astrometric satellite Gaia is scanning the whole sky with unprecedented accuracy up to a few muas level. However, Gaia's two fields of view observations strategy may introduce a parallax bias in the Gaia catalog. Since it presents no significant parallax, quasar is perfect nature object to detect such bias. More importantly, quasars can be used to construct a Celestial Reference Frame in the optical wavelengths in Gaia mission. In this paper, we compile the most reliable quasars existing in literatures. The final compilation (designated as Known Quasars Catalog for Gaia mission, KQCG) contains 1843850 objects, among of them, 797632 objects are found in Gaia DR1 after cross-identifications. This catalog will be very useful in Gaia mission

Time variation of Newton's gravitational constant in superstring theories

Journal ArticleThe present time variation of coupling constants in superstring theories with currently favorable internal backgrounds critically depends on the shape of the potential for the size of the internal space. If the potential is almost flat, as in perturbation theory to all orders, the value of G/G for Newton's gravitational constant is calculable and estimated to be - 1x10- 11 ± yr-1 . If the potential has a minimum with finite curvature due to unknown nonperturbative effects, G/G will become unobservably small. Improvement of the measurement of G/ G would discriminate between the two situations. Problems with the time variation of other coupling constants are also discussed

Absence of (1,0) supersymmetry anomaly in world-sheet gauge theories: a purely cohomological proof

Journal ArticleA purely cohomological proof is given for the absence of the (1,0) supersymmetry anomaly in gauge theories on a world sheet. In particular, it is shown that generalized cohomological approaches to anomalies in supersymmetric gauge theory, either formulated in whole superconnection space or only in the Wess-Zumino-gauge surface, yield results which agree with those obtained by noncohomological field-theoretical methods. We argue that the success of the cohomological arguments implies that there should be a generalization of (family) index theorem in the supersymmetric cases