41 research outputs found
Two New Characterizations of Path Graphs
Path graphs are intersection graphs of paths in a tree. We start from the
characterization of path graphs by Monma and Wei [C.L.~Monma,~and~V.K.~Wei,
Intersection Graphs of Paths in a Tree, J. Combin. Theory Ser. B, 41:2 (1986)
141--181] and we reduce it to some 2-colorings subproblems, obtaining the first
characterization that directly leads to a polynomial recognition algorithm.
Then we introduce the collection of the attachedness graphs of a graph and we
exhibit a list of minimal forbidden 2-edge colored subgraphs in each of the
attachedness graph.Comment: 18 pages, 6 figure
Leptogenesis and rescattering in supersymmetric models
The observed baryon asymmetry of the Universe can be due to the
violating decay of heavy right handed (s)neutrinos. The amount of the asymmetry
depends crucially on their number density. If the (s)neutrinos are generated
thermally, in supersymmetric models there is limited parameter space leading to
enough baryons. For this reason, several alternative mechanisms have been
proposed. We discuss the nonperturbative production of sneutrino quanta by a
direct coupling to the inflaton. This production dominates over the
corresponding creation of neutrinos, and it can easily (i.e. even for a rather
small inflaton-sneutrino coupling) lead to a sufficient baryon asymmetry. We
then study the amplification of MSSM degrees of freedom, via their coupling to
the sneutrinos, during the rescattering phase which follows the nonperturbative
production. This process, which mainly influences the (MSSM) flat
directions, is very efficient as long as the sneutrinos quanta are in the
relativistic regime. The rapid amplification of the light degrees of freedom
may potentially lead to a gravitino problem. We estimate the gravitino
production by means of a perturbative calculation, discussing the regime in
which we expect it to be reliable.Comment: (20 pages, 6 figures), references added, typos corrected. Final
version in revte
A New Characterization of Path Graphs
In this paper we give a "good characterization" of path graphs, namely, we prove that path graph
membership is in without resorting to existing polynomial time
algorithms. The characterization is given in terms of the collection of the
emph{attachedness graphs} of a graph, a novel device to deal with the
connected components of a graph after the removal of clique separators. On the
one hand, the characterization refines and simplifies the characterization of
path graphs due to Monma and Wei [C.L.~Monma,~and~V.K.~Wei, Intersection
{G}raphs of {P}aths in a {T}ree, J. Combin. Theory Ser. B, 41:2 (1986)
141--181], which we build on, by reducing a constrained vertex coloring problem
defined on the emph{attachedness graphs} to a vertex 2-coloring problem on the
same graphs. On the other hand, the characterization allows us to exhibit two
exhaustive lists of obstructions to path graph membership in the form of
minimal forbidden induced/partial 2-edge colored subgraphs in each of the
emph{attachedness graphs}