相关论文: The bunkbed conjecture is false

The paper disproves a basic theorem on quasi-birth-and-death processes given in [M. F. Neuts (1995). Matrix Geometric Solutions in Stochastic Models: An Algorithmic Approach. Dover, New York].

In 1993 Stanley showed that if a simplicial complex is acyclic over some field, then its face poset can be decomposed into disjoint rank $1$ boolean intervals whose minimal faces together form a subcomplex. Stanley further conjectured that…

Konig's theorem states that the covering number and the matching number of a bipartite graph are equal. We prove a generalisation of this result, in which each point in one side of the graph is replaced by a subtree of a given tree. The…

By considering suitable axially symmetric slices on the Kruskal spacetime, we construct counterexamples to a recent version of the Penrose inequality in terms of so-called generalized apparent horizons.

B\'ar\'any, Kalai, and Meshulam recently obtained a topological Tverberg-type theorem for matroids, which guarantees multiple coincidences for continuous maps from a matroid complex to d-dimensional Euclidean space, if the matroid has…

A typical decomposition question asks whether the edges of some graph $G$ can be partitioned into disjoint copies of another graph $H$. One of the oldest and best known conjectures in this area, posed by Ringel in 1963, concerns the…

In 1990, Hendry conjectured that every Hamiltonian chordal graph is cycle extendible; that is, the vertices of any non-Hamiltonian cycle are contained in a cycle of length one greater. We disprove this conjecture by constructing…

A double disk bundle is any smooth closed manifold obtained as the union of the total spaces of two disk bundles, glued together along their common boundary. The Double Soul Conjecture asserts that a closed simply connected manifold…

The Erd\H{o}s-Szekeres conjecture states that any set of more than $2^{n-2}$ points in the plane with no three on a line contains the vertices of a convex $n$-gon. Erd\H{o}s, Tuza, and Valtr strengthened the conjecture by stating that any…

A recent conjecture by C. Carlet on the sum-freedom of the binary multiplicative inverse function can be stated as follows: For each pair of positive integers $(n,k)$ with $3\le k\le n-3$, there is a $k$-dimensional $\Bbb F_2$-subspace $E$…

A conjecture by Bollob\'as from 1995 (which is a weakenning of the famous Tree Packing Conjecture by Gy\'arf\'as from 1976) states that any set of $k$ trees $T_n,T_{n-1},\dots,T_{n-k+1}$, such that $T_{n-i}$ has $n-i$ vertices, pack into…

Reed Conjecture is open for more than 20 years now. Here we prove that Reed Conjecture is valid for (1) {P4UnionK1, Kite}-free graphs (2) {Chair, Kite}-free graphs (3) {K2UnionK2complement , H}-free graphs and (4) {2K2, M}-free graphs where…

We introduce a new variant of the coarse Baum-Connes conjecture designed to tackle coarsely disconnected metric spaces called the boundary coarse Baum-Connes conjecture. We prove this conjecture for many coarsely disconnected spaces that…

In this paper we propose counterexamples to the Geometrization Conjecture and the Elliptization Conjecture.

In 1962 P\'osa conjectured that every graph G on n vertices with minimum degree at least 2n/3 contains the square of a hamiltonian cycle. In 1996 Fan and Kierstead proved the path version of P\'osa's Conjecture. They also proved that it…

We prove a conjecture of Toponogov on complete convex planes, namely that such planes must contain an umbilic point, albeit at infinity. Our proof is indirect. It uses Fredholm regularity of an associated Riemann-Hilbert boundary value…

The conjecture by Steklov was solved negatively by Rakhmanov in 1979. His original proof was based on the formula for orthogonal polynomial obtained by adding point masses to the measure of orthogonality. In this note, we show how this…

A conjecture of Verstra\"ete states that for any fixed $\ell < k$ there exists a positive constant $c$ such that any $C_{2k}$-free graph $G$ contains a $C_{2\ell}$-free subgraph with at least $c |E(G)|$ edges. For $\ell = 2$, this…

In 2008 Karasev conjectured that for every set of $r$ blue lines, $r$ green lines, and $r$ red lines in the plane, there exists a partition of them into $r$ colorful triples whose induced triangles intersect. We disprove this conjecture for…

The classical Shafarevich conjecture predicts that the universal cover of a complex smooth projective variety $X$ is holomorphically convex. In this paper, we propose a refinement of this conjecture for varieties defined over the reals. In…