1,116 research outputs found
Some characterizations of the exceptional planar embedding of W(2)
AbstractIn this paper, we study the representation of W(2) in PG(2,4) related to a hyperoval. We provide a group-theoretic characterization and some geometric ones
Steinitz Theorems for Orthogonal Polyhedra
We define a simple orthogonal polyhedron to be a three-dimensional polyhedron
with the topology of a sphere in which three mutually-perpendicular edges meet
at each vertex. By analogy to Steinitz's theorem characterizing the graphs of
convex polyhedra, we find graph-theoretic characterizations of three classes of
simple orthogonal polyhedra: corner polyhedra, which can be drawn by isometric
projection in the plane with only one hidden vertex, xyz polyhedra, in which
each axis-parallel line through a vertex contains exactly one other vertex, and
arbitrary simple orthogonal polyhedra. In particular, the graphs of xyz
polyhedra are exactly the bipartite cubic polyhedral graphs, and every
bipartite cubic polyhedral graph with a 4-connected dual graph is the graph of
a corner polyhedron. Based on our characterizations we find efficient
algorithms for constructing orthogonal polyhedra from their graphs.Comment: 48 pages, 31 figure
Combinatorial RNA Design: Designability and Structure-Approximating Algorithm
In this work, we consider the Combinatorial RNA Design problem, a minimal
instance of the RNA design problem which aims at finding a sequence that admits
a given target as its unique base pair maximizing structure. We provide
complete characterizations for the structures that can be designed using
restricted alphabets. Under a classic four-letter alphabet, we provide a
complete characterization of designable structures without unpaired bases. When
unpaired bases are allowed, we provide partial characterizations for classes of
designable/undesignable structures, and show that the class of designable
structures is closed under the stutter operation. Membership of a given
structure to any of the classes can be tested in linear time and, for positive
instances, a solution can be found in linear time. Finally, we consider a
structure-approximating version of the problem that allows to extend bands
(helices) and, assuming that the input structure avoids two motifs, we provide
a linear-time algorithm that produces a designable structure with at most twice
more base pairs than the input structure.Comment: CPM - 26th Annual Symposium on Combinatorial Pattern Matching, Jun
2015, Ischia Island, Italy. LNCS, 201
On the cone of effective 2-cycles on
Fulton's question about effective -cycles on for
can be answered negatively by appropriately lifting to
the Keel-Vermeire divisors on . In
this paper we focus on the case of -cycles on , and we
prove that the -dimensional boundary strata together with the lifts of the
Keel-Vermeire divisors are not enough to generate the cone of effective
-cycles. We do this by providing examples of effective -cycles on
that cannot be written as an effective combination of the
aforementioned -cycles. These examples are inspired by a blow up
construction of Castravet and Tevelev.Comment: 22 pages, 4 figures. Final version. Minor corrections. To appear in
the European Journal of Mathematic
Cohen-Macaulay Du Bois singularities with a torus action of complexity one
Using Altmann-Hausen-S\"u\ss\ description of T-varieties via divisorial fans
and K\'ovacs-Schwede-Smith characterization of Du Bois singularities we prove
that any rational T-variety of complexity one which is Cohen-Macaulay and Du
Bois has rational singularities. In higher complexity, we prove an analogous
result in the case where the Chow quotient of the T-variety has Picard rank one
and trivial geometric genus.Comment: 16 page
Combinatorial RNA Design Designability and Structure-Approximating Algorithm in Watson-Crick and Nussinov-Jacobson Energy Models
We consider the Combinatorial RNA Design problem, a minimal instance of RNA
design where one must produce an RNA sequence that adopts a given secondary
structure as its minimal free-energy structure. We consider two free-energy
models where the contributions of base pairs are additive and independent: the
purely combinatorial Watson-Crick model, which only allows equally-contributing
A -- U and C -- G base pairs, and the real-valued Nussinov-Jacobson model,
which associates arbitrary energies to A -- U, C -- G and G -- U base pairs. We
first provide a complete characterization of designable structures using
restricted alphabets and, in the four-letter alphabet, provide a complete
characterization for designable structures without unpaired bases. When
unpaired bases are allowed, we characterize extensive classes of
(non-)designable structures, and prove the closure of the set of designable
structures under the stutter operation. Membership of a given structure to any
of the classes can be tested in (n) time, including the generation of a
solution sequence for positive instances. Finally, we consider a
structure-approximating relaxation of the design, and provide a (n)
algorithm which, given a structure S that avoids two trivially non-designable
motifs, transforms S into a designable structure constructively by adding at
most one base-pair to each of its stems.Comment: To appea
Three-coloring triangle-free graphs on surfaces II. 4-critical graphs in a disk
Let G be a plane graph of girth at least five. We show that if there exists a
3-coloring phi of a cycle C of G that does not extend to a 3-coloring of G,
then G has a subgraph H on O(|C|) vertices that also has no 3-coloring
extending phi. This is asymptotically best possible and improves a previous
bound of Thomassen. In the next paper of the series we will use this result and
the attendant theory to prove a generalization to graphs on surfaces with
several precolored cycles.Comment: 48 pages, 4 figures This version: Revised according to reviewer
comment
An extensive English language bibliography on graph theory and its applications, supplement 1
Graph theory and its applications - bibliography, supplement
- …