809 research outputs found
Quark and lepton masses and mixing from a gauged SU(3)_F family symmetry with a light O(eV) sterile Dirac neutrino
In the framework of a complete vector-like and universal gauged SU(3)_F
family symmetry, we report a global region in the parameter space where this
approach can account for a realistic spectrum of quark masses and mixing in a 4
x 4 non-unitary V_{CKM}, as well as for the known charged lepton masses and the
squared neutrino mass differences reported from neutrino oscillation
experiments. The family symmetry is broken spontaneously in two
stages by heavy SM singlet scalars, whose hierarchy of scales yield and
approximate SU(2)_F global symmetry associated to the almost degenerate boson
masses of the order of the lower scale of the SU(3)_F SSB. The gauge symmetry,
the fermion content, and the transformation of the scalar fields, all together,
avoid Yukawa couplings between SM fermions. Therefore, in this scenario
ordinary heavy fermions, top and bottom quarks and tau lepton, become massive
at tree level from Dirac See-saw mechanisms, while light fermions, including
light neutrinos, obtain masses from radiative corrections mediated by the
massive gauge bosons of the SU(3)_F family symmetry. The displayed fit
parameter space region solution for fermion masses and mixing yield the
vector-like fermion masses: M_D \approx 3.2 \,TeV, M_U \approx 6.9 \,TeV, M_E
\approx 21.6 \,TeV, SU(2)_F family gauge boson masses of ,
and the squared neutrino mass differences: m_2^2-m_1^2 \approx 7.5 x
10^{-5}\;eV^2, m_3^2-m_2^2 \approx 2.2 x 10^{-3}\;eV^2, m_4^2-m_1^2 \approx
0.82\;eV^2.Comment: 19 pages, 1 figure, Contribution to Proceedings of the 19th Workshop
"What Comes Beyond the Standard Models", July 11-19, Bled, Slovenia. arXiv
admin note: substantial text overlap with arXiv:1602.08212, arXiv:1212.457
Solving the kernel perfect problem by (simple) forbidden subdigraphs for digraphs in some families of generalized tournaments and generalized bipartite tournaments
A digraph such that every proper induced subdigraph has a kernel is said to
be \emph{kernel perfect} (KP for short) (\emph{critical kernel imperfect} (CKI
for short) resp.) if the digraph has a kernel (does not have a kernel resp.).
The unique CKI-tournament is and the unique
KP-tournaments are the transitive tournaments, however bipartite tournaments
are KP. In this paper we characterize the CKI- and KP-digraphs for the
following families of digraphs: locally in-/out-semicomplete, asymmetric
arc-locally in-/out-semicomplete, asymmetric -quasi-transitive and
asymmetric -anti-quasi-transitive -free and we state that the problem
of determining whether a digraph of one of these families is CKI is polynomial,
giving a solution to a problem closely related to the following conjecture
posted by Bang-Jensen in 1998: the kernel problem is polynomially solvable for
locally in-semicomplete digraphs.Comment: 13 pages and 5 figure
New Bounds for the Dichromatic Number of a Digraph
The chromatic number of a graph , denoted by , is the minimum
such that admits a -coloring of its vertex set in such a way that each
color class is an independent set (a set of pairwise non-adjacent vertices).
The dichromatic number of a digraph , denoted by , is the minimum
such that admits a -coloring of its vertex set in such a way that
each color class is acyclic.
In 1976, Bondy proved that the chromatic number of a digraph is at most
its circumference, the length of a longest cycle.
Given a digraph , we will construct three different graphs whose chromatic
numbers bound .
Moreover, we prove: i) for integers , and with and for each , that if all
cycles in have length modulo for some ,
then ; ii) if has girth and there are integers
and , with such that contains no cycle of length
modulo for each , then ;
iii) if has girth , the length of a shortest cycle, and circumference
, then , which improves,
substantially, the bound proposed by Bondy. Our results show that if we have
more information about the lengths of cycles in a digraph, then we can improve
the bounds for the dichromatic number known until now.Comment: 14 page
Alternating Hamiltonian cycles in -edge-colored multigraphs
A path (cycle) in a -edge-colored multigraph is alternating if no two
consecutive edges have the same color. The problem of determining the existence
of alternating Hamiltonian paths and cycles in -edge-colored multigraphs is
an -complete problem and it has been studied by several authors.
In Bang-Jensen and Gutin's book "Digraphs: Theory, Algorithms and
Applications", it is devoted one chapter to survey the last results on this
topic. Most results on the existence of alternating Hamiltonian paths and
cycles concern on complete and bipartite complete multigraphs and a few ones on
multigraphs with high monochromatic degrees or regular monochromatic subgraphs.
In this work, we use a different approach imposing local conditions on the
multigraphs and it is worthwhile to notice that the class of multigraphs we
deal with is much larger than, and includes, complete multigraphs, and we
provide a full characterization of this class.
Given a -edge-colored multigraph , we say that is
--closed (resp. --closed)} if for every
monochromatic (resp. non-monochromatic) -path , there
exists an edge between and . In this work we provide the following
characterization: A --closed multigraph has an alternating
Hamiltonian cycle if and only if it is color-connected and it has an
alternating cycle factor.
Furthermore, we construct an infinite family of --closed
graphs, color-connected, with an alternating cycle factor, and with no
alternating Hamiltonian cycle.Comment: 15 pages, 20 figure
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