Coverings of the complete (di-)graph with n vertices by complete bipartite (di-)graphs with n vertices I

Let n be an integer, n ? 2. A set $\text{M}$_n of complete bipartite (di-)graphs with n vertices is called a critical covering of the complete (di-)graph with n vertices if and only if the complete (di-)graph is covered by the (di-)graphs of $\text{M}$_n, but of no proper subset of $\text{M}$_n. All possible cardinalities of critical coverings $\text{M}$_n are determined for all integers n and for undirected as well as directed graphs.     

Lepton energy spectra in e+e− annihilation and other processes

An analysis is presented of the single inclusive lepton spectra expected from the decay of charmed hadrons or heavier particles with new flavors produced in e⁺e^? annihilation. Extremely soft spectra are found, in contrast to the heavy lepton signal. Good detection efficiency at low momentum will therefore continue to be important in future experiments. A range of plausible inclusive D meson spectra abstracted from a parton fragmentation picture is employed. The model is applicable to other processes.     

U-spin symmetry in doubly Cabibbo-suppressed charmed meson decays

We prove a U-spin amplitude triangle relation among doubly Cabibbo-suppressed (DCS) charmed meson decays, D⁰→K⁺π⁻,D⁰→K⁰π⁰ and D⁺_s→K⁰K⁺, congruent to an isospin relation among corresponding Cabibbo-favored (CF) decays. U-spin breaking in relative phases between CF and DCS amplitudes affects time-dependent studies of D⁰– mixing. Comparison of final state phase patterns in DCS and CF amplitude triangles, which can shed some light on these phases, is carried out in a phenomenological framework incorporating resonance contributions.     

On Sperner families in which no k sets have an empty intersection, II

Let n_c,d(r, k) denote the maximal cardinality of Sperner families (i.e., XY for all X, Y ε ) on an r-element set satisfying c X d for all X ε and in which no k sets have an empty intersection. n_c,d(r, k) was determined by Frankl (J. Combin. Theory Ser. A 20 (1976), 1–11) if c r/k, and, if c = 0 and d = r, by Frankl and the author (J. Combin. Theory Ser. A 28 (1980), 54–63; Acta Cybernet. 4 (1978), 213–220 for all r and k with exception of 60 values of r if k = 3. In this paper we solve the problem of determination of n_c,d(r, 3) in nearly all unknown cases. In particular, we obtain n_0,r(r, 3) for 33 of the exceptional cases.     

Ambiguities in zeroth order fermion mass matrices

The six quark Weinberg-Salam model with the symmetry of the three generation permutation group S₃ has an extra O(2) pseudosymmetry when the Higgs fields lie in an S₃ doublet. We use this model as a prototype to question the derivation of zeroth order relations between fermion mixing angles and fermion masses.     

On Orthogonal Double Covers of Graphs

An orthogonal double cover (ODC) is a collection of n spanning subgraphs(pages) of the complete graph K _n such that they cover every edge of the completegraph twice and the intersection of any two of them contains exactly one edge. If all the pages are isomorphic tosome graph G, we speak of an ODC by G. ODCs have been studied for almost 25 years, and existenceresults have been derived for many graph classes. We present an overview of the current state of research alongwith some new results and generalizations. As will be obvious, progress made in the last 10 years is in many waysrelated to the work of Ron Mullin. So it is natural and with pleasure that we dedicate this article to Ron, on theoccasion of his 65th birthday.