相关论文: Towards a Splitter Theorem for Internally $4$-conn…

We study an explicit construction of planar open books with four binding components on any three-manifold which is given by integral surgery on three component pure braid closures. This construction is general, indeed any planar open book…

We show that an adjoint of a loopless matroid is connected if and only if it itself is connected. Our first goal is to study the adjoint of modular matroids. We prove that a modular matroid has only one adjoint (up to isomorphism) which can…

We show that every $3$-connected $K_{2,\ell}$-minor free graph with minimum degree at least $4$ has maximum degree at most $7\ell$. As a consequence, we show that every 3-connected $K_{2,\ell}$-minor free graph with minimum degree at least…

It is well known that a matroid L is a lift of a matroid M if and only if every circuit of L is the union of some circuits of M. In this paper we give a simpler proof of this important theorem. We also described a discrete homotopy theorem…

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…

Let $G$ and $H$ be simple 3-connected graphs such that $G$ has an $H$-minor. An edge $e$ in $G$ is called {\it $H$-deletable} if $G\backslash e$ is 3-connected and has an $H$-minor. The main result in this paper establishes that, if $G$ has…

We prove that if $ M $ and $ N $ are finitary matroids on a common countable edge set $ E $ then they admit a common independent set $I $ such that there is a bipartition $ E=E_{M}\cup E_{N} $ for which $ I\cap E_M $ spans $ E_M $ in $ M $…

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…

Almost $4$-connectivity is a weakening of $4$-connectivity which allows for vertices of degree three. In this paper we prove the following theorem. Let $G$ be an almost $4$-connected triangle-free planar graph, and let $H$ be an almost…

A particular two-parameter class of little string theories can be described by $M$ parallel M5-branes probing a transverse affine $A_{N-1}$ singularity. We previously discussed the duality between the theories labelled by $(N,M)$ and…

We report crystal structure, electronic structure, and magnetism of manganese tetraboride, MnB4, synthesized under high-pressure high-temperature conditions. In contrast to superconducting FeB4 and metallic CrB4, which are both…

A $3$-connected graph is minimally 3-connected if removal of any edge destroys 3-connectivity. We present an algorithm for constructing minimally 3-connected graphs based on the results in (Dawes, JCTB 40, 159-168, 1986) using two…

Let $ E $ be a possibly infinite set and let $ M $ and $ N $ be matroids defined on $ E $. We say that the pair $ \{ M,N \} $ has the Intersection property if $ M $ and $ N $ share an independent set $ I $ admitting a bipartition $…

This letter is an attempt to carry out a first-principle computation in M-theory using the point of view that the eleven-dimensional membrane gives the fundamental degrees of freedom of M-theory. Our aim is to derive the exact BPS $R^4$…

Inspired by a recent result of Brakensiek et al. that symmetric tensor matroids and rigidity matroids are linked by matroid duality, we define abstract symmetric tensor matroids as a dual concept to abstract rigidity matroids and establish…

The closure $\textrm{cl}(R)$ of a consistent set $R$ of triples (rooted binary trees on three leaves) provides essential information about tree-like relations that are shown by any supertree that displays all triples in $R$. In this…

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 experimentally demonstrate stimulated four-wave mixing in two linearly uncoupled integrated Si$_3$N$_4$ micro-resonators. In our structure the resonance combs of each resonator can be tuned independently, with the energy transfer from…

A link in the 3-sphere is called (smoothly) slice if its components bound disjoint smoothly embedded disks in the 4-ball. More generally, given a 4-manifold M with a distinguished circle in its boundary, a link in the 3-sphere is called…

We prove a splitter theorem for tight multimatroids, generalizing the corresponding result for matroids, obtained independently by Brylawski and Seymour. Further corollaries give splitter theorems for delta-matroids and ribbon graphs.