Heavy paths, light stars, and big melons

Heavy paths, light stars, and big melons

Big Bang and Heavy Particles

A possibility of existence of ultra-heavy (quasi)stable particles, mechanisms leading to their large lifetime , their production in the early universe, and cosmological manifestations are reviewed.

Saturation spectrum of paths and stars

24 A graph G is H-saturated if H is not a subgraph of G but the addition of any edge from G to G 25 results in a copy of H. The minimum size of an H-saturated graph on n vertices is denoted sat(n,H), 26 while the maximum size is the well studied extremal numbers, ex(n,H). The saturation spectrum for 27 a graph H is the set of sizes of H saturated graphs between sat(n,H) and ex(n,H). In this pap...

Heavy paths and cycles in weighted graphs

A weighted graph is a graph in which each edge e is assigned a non-negative number w(e), called the weight of e. In this paper, some theorems on the existence of long paths and cycles in unweighted graphs are generalized to heavy paths and cycles in weighted graphs.

Heavy calcium in CP stars★

Large wavelength shifts of infrared triplet lines of Ca ii have been observed in the spectra of HgMn and magnetic Ap stars. They have been attributed to the heavy calcium isotopes, including Ca. One member of the triplet, λ8542, had been either unavailable, or of poor quality in earlier spectra. The present material shows conclusively that the stellar λ8542 shifts are consistent with an interpr...