What must and what need not be contained in a graph of uncountable chromatic number?

We investigate the following problem: What countable graphs must a graph of uncountable chromatic number contain? We define two graphsΓ andΔ which are very similar and we show thatΓ is contained in every graph of uncountable chromatic number, whileΔ is (consistently) not.     

Supersaturated graphs and hypergraphs

We shall consider graphs (hypergraphs) without loops and multiple edges. Let ? be a family of so called prohibited graphs and ex (n, ?) denote the maximum number of edges (hyperedges) a graph (hypergraph) onn vertices can have without containing subgraphs from ?. A graph (hyper-graph) will be called supersaturated if it has more edges than ex (n, ?). IfG hasn vertices and ex (n, ?)+k edges (hyperedges), then it always contains prohibited subgraphs. The basic question investigated here is: At least how many copies ofL ε ? must occur in a graphG ⁿ onn vertices with ex (n, ?)+k edges (hyperedges)?     

NMR studies of the chalcogen analogues of benzofuran. IV—Proton,carbon-13 and selenium-77 magnetic resonance in nitrobenzo[b]selenophenes

The ¹H, ¹³C and ⁷⁷Se chemical shifts have been measured for mononitrobenzo[ b ]selenophenes. For the homocyclic nuclei, the observed ¹H- and ¹³C-values calculated from the empirical increments of nitrobenzene. Anomalous effects are observed in the 2- and 3-substituted derivatives and the nature of the Se? NO₂ interactions in the former is discussed. ⁷⁷Se chemical shifts of the 4-, 5- and 7-nitro derivatives are approximately correlated with the CNDO calculated electron densities; they also compare well with those of selenoanisoles and other phenyl alkyl selenides. The chemical shifts are also compared with the corresponding values in other heterocycles containing a selenophene moiety.     

Stationary vacuum fields with a conformally flat three-space I. General theory

A generalized notion of conformastat space-times is introduced in relativity theory. In this sense, the conformastat space-time is stationary with the three-space of timelike Killing trajectories being conformally flat. A 3+1 decomposition of the field equations is given, and two classes of nonstatic conformastat vacuum fields are exhaustively investigated. The resulting three metrics form a NUT-type extension of the solution of the static conformastat vacuum problem. We conjecture that all conformastat vacuum space-times are axially symmetric.     

A class of Hamiltonian regular graphs

In this paper, we show that n ? 4 and if G is a 2-connected graph with 2n or 2n?1 vertices which is regular of degree n?2, then G is Hamiltonian if and only if G is not the Petersen graph.     

The i.r. spectrum of curium-244

The spectrum of curium-244 has been observed on the high resolution Fourier-transform spectrometer at Laboratoire Aimé Cotton. An electrodeless lamp containing 50 μg of CmI₃ was run for 12 hr and 800,000 points were taken. A total of 1743 lines have been ascribed to curium and 87% of the lines have been assigned to transitions between known energy levels.