Related papers: Towards a Splitter Theorem for Internally $4$-conn…
Let $M$ be a matroid defined on a finite set $E$ and $L\subset E$. $L$ is locked in $M$ if $M|L$ and $M^*|(E\backslash L)$ are 2-connected, and $min\{r(L), r^*(E\backslash L)\} \geq 2$. Locked subsets characterize nontrivial facets of the…
Many important enumerative invariants of a matroid can be obtained from its Tutte polynomial, and many more are determined by two stronger invariants, the $\mathcal{G}$-invariant and the configuration of the matroid. We show that the same…
If and only if the small neutrino mixing sine s_13 is put zero, the effective neutrino mass matrix M with any mixing sines s_12 and s_23 is invariant under a cyclic group Z_2 of the order two and -- in the limit of m_2 - m_1 --> 0 -- also…
A connected graph is 4-connected if it contains at least five vertices and removing any three of them does not disconnect it. A frequent preprocessing step in graph drawing is to decompose a plane graph into its 4-connected components and…
We show that for any regular matroid on $m$ elements and any $\alpha \geq 1$, the number of $\alpha$-minimum circuits, or circuits whose size is at most an $\alpha$-multiple of the minimum size of a circuit in the matroid is bounded by…
Split matroids form a minor-closed class of matroids, and are defined by placing conditions on the system of split hyperplanes in the matroid base polytope. They can equivalently be defined in terms of structural properties involving cyclic…
In mathematics and computer science, connectivity is one of the basic concepts of matroid theory: it asks for the minimum number of elements which need to be removed to disconnect the remaining nodes from each other. It is closely related…
The splitting operation on a $p$-matroid does not necessarily preserve connectivity. It is observed that there exists a single element extension of the splitting matroid which is connected. In this paper, we define the element splitting…
The change of a material's electrical resistance (R) in response to an external magnetic field (B) provides subtle information for the characterization of its electronic properties and has found applications in sensor and storage related…
Consider a random $n\times m$ matrix $A$ over the finite field of order $q$ where every column has precisely $k$ nonzero elements, and let $M[A]$ be the matroid represented by $A$. In the case that q=2, Cooper, Frieze and Pegden (RS\&A…
In this work we provide a decomposition theorem for the class of quaternary and non-binary signed-graphic matroids. This generalizes previous results for binary signed-graphic matroids and graphic matroids, and it provides the theoretical…
Whitney proved in 1931 that every 4-connected planar triangulation is hamiltonian. Later in 1979, Hakimi, Schmeichel and Thomassen conjectured that every such triangulation on $n$ vertices has at least $2(n - 2)(n - 4)$ hamiltonian cycles.…
Given any connected, open 3-manifold $U$ having finitely many ends, a non-compact 3-manifold $M$ is constructed having the following properties: the interior of $M$ is homeomorphic to $U$; the boundary of $M$ is the disjoint union of…
A subset $S$ of $\{0,1,...,2t-1\}^n$ is called a $t$-fold MDS code if every line in each of $n$ base directions contains exactly $t$ elements of $S$. The adjacency graph of a $t$-fold MDS code is not connected if and only if the…
Results on the existence of various types of spanning subgraphs of graphs are milestones in structural graph theory and have been diversified in several directions. In the present paper, we consider "local" versions of such statements. In…
We show that there exist split, orientable, 2-component surface-links in $S^4$ with non-isotopic splitting spheres in their complements. In particular, for non-negative integers $m,n$ with $m\ge 4$, the unlink $L_{m,n}$ consisting of one…
We present a construction of the integrand of the correlation function of four stress-tensor multiplets in N=4 SYM at weak coupling. It does not rely on Feynman diagrams and makes use of the recently discovered symmetry of the integrand…
We have investigated from first-principles an electronic structure and magnetism in MnB4 compound with experimentally observed orthorhombic C12/m1 structure. It is found that Mn tetra-borides (MnB4) is found to have metallic ground state…
For any minor-closed class of matroids over a fixed finite field, we state an exact structural characterization for the sufficiently connected matroids in the class. We also state a number of conjectures that might be approachable using the…
We are interested in contractible n-manifolds M which "split" as M = A union B where A,B, and A intersect B are all homeomorphic to Euclidean n-space (such M are called open n-splitters) or A,B, and A intersect B are all homeomorphic to the…