Subdivisions of graphs with large minimum degree

We prove a theorem on path systems implying the conjecture of Bollobás that there exists a function f(k, m) (where k and m are natural numbers) satisfying the following: For each graph G of minimum degree at least f(k, m) there exists a graph H of minimum degree at least k such that G contains the graph obtained from H by subdividing each edge m times.     

Girth in graphs

It is shown that a graph of large girth and minimum degree at least 3 share many properties with a graph of large minimum degree. For example, it has a contraction containing a large complete graph, it contains a subgraph of large cyclic vertex-connectivity (a property which guarantees, e.g., that many prescribed independent edges are in a common cycle), it contains cycles of all even lengths modulo a prescribed natural number, and it contains many disjoint cycles of the same length. The analogous results for graphs of large minimum degree are due to Mader (Math. Ann.194 (1971), 295–312; Abh. Math. Sem. Univ. Hamburg37 (1972), 86–97), Woodall (J. Combin. Theory Ser. B22 (1977), 274–278), Bollobás (Bull. London Math. Soc.9 (1977), 97–98) and Häggkvist (Equicardinal disjoint cycles in sparse graphs, to appear). Also, a graph of large girth and minimum degree at least 3 has a cycle with many chords. An analogous result for graphs of chromatic number at least 4 has been announced by Voss (J. Combin. Theory Ser. B32 (1982), 264–285).     

Cycles in digraphs– a survey

The main subjects of this survey paper are Hamiltonian cycles, cycles of prescribed lengths, cycles in tournaments, and partitions, packings, and coverings by cycles. Several unsolved problems and a bibliography are included.     

Strongly self-complementary and hereditarily isomorphic tournaments

A tournament is strongly self-complementary if every subtournament is self-complementary. TournamentsR, B defined on the same vertex setV are hereditarily isomorphic if for every subsetA ofV, the induced subtournamentsR(A) andB(A) are isomorphic. We determine all strongly self-complementary tournaments and apply this result to characterize the paris of hereditarily isomorphic tournaments.     

Note on circuits containing specified edges

If L is a set of at most l disjoint edges in a $\text{[}\text{3}\text{2}\text{l?}\text{1}\text{2}\text{]-}\text{connected}$ graph, then there is a circuit containing all edges of L.     

Atomic absorption spectrometric determination of thirteen minor and trace metals in phosphate rock concentrates

Atomic absorption spectrometric methods are described for the determination of thirteen minor and trace elements in phosphate rock concentrates from Florida (U S.A.), Kola (U.S.S.R.) and Morocco. The techniques employed are atomization of solid or liquid samples in two types of graphite furnace, and conventional atomization in the flame or the cold-vapour cell.     

Absorption and Oxidation of Nitrogen Oxide in Ionic Liquids

A new strategy for capturing nitrogen oxide, NO, from the gas phase is presented. Dilute NO gas is removed from the gas phase by ionic liquids under ambient conditions. The nitrate anion of the ionic liquid catalyzes the oxidation of NO to nitric acid by atmospheric oxygen in the presence of water. The nitric acid is absorbed in the ionic liquid up to approximately one mole HNO₃ per mole of the ionic liquid due to the formation of hydrogen bonds. The nitric acid can be desorbed by heating, thereby regenerating the ionic liquid with excellent reproducibility. Here, time‐resolved in‐situ spectroscopic investigations of the reaction and products are presented. The procedure reveals a new vision for removing the pollutant NO by absorption into a non‐volatile liquid and converting it into a useful bulk chemical, that is, HNO₃.     

Ultrasound-Promoted Dimerization of Benzylic Halides

Simple and straightforward coupling of benzylic compounds was achieved by sonicating benzylic halides in the presence of magnesium.