相关论文: The bunkbed conjecture remains true when gluing al…
The 2-Decomposition Conjecture, equivalent to the 3-Decomposition Conjecture stated in 2011 by Hoffmann-Ostenhof, claims that every connected graph $G$ with vertices of degree 2 and 3, for which $G \setminus E(C)$ is disconnected for every…
A gluing of two rooted trees is an identification of their leaves and un-subdivision of the resulting 2-valent vertices. A gluing of two rooted trees is subdivergence free if it has no 2-edge cuts with both roots on the same side of the…
We confirm Jones' Conjecture for subcubic graphs. Namely, if a subcubic planar graph does not contain $k+1$ vertex-disjoint cycles, then it suffices to delete $2k$ vertices to obtain a forest.
In this paper we discuss the sufficient and necessary conditions for multiple Alexandrov spaces being glued to an Alexandrov space. We propose a Gluing Conjecture, which says that the finite gluing of Alexandrov spaces is an Alexandrov…
Recently, it has been proven that a tensegrity framework that arises from coning the one-skeleton of a convex polytope is rigid. Since such frameworks are not always infinitesimally rigid, this leaves open the question as to whether they…
We propose the following conjecture: For every fixed $\alpha\in [0,\frac 13)$, each graph of minimum degree at least $(1+\alpha)\frac k2$ and maximum degree at least $2(1-\alpha)k$ contains each tree with $k$ edges as a subgraph. Our main…
Consider moduli schemes of vector bundles over a smooth projective curve endowed with parabolic structures over a marked point. Boden and Hu observed that a slight variation of the weights leads to a desingularisation of the moduli scheme,…
In this paper, we apply liaison theory to the Eisenbud-Green-Harris conjecture and prove that the conjecture holds for a certain subclass of homogeneous ideals in the linkage class of a complete intersection ideal. In the case of three…
We briefly review an open conjecture about Higgs bundles that are semistable with after pulling back to any curve, and prove it in the rank 2 case. We also prove a set of inequalities holding for H-nef Higgs bundles that generalize some of…
Berge Conjecture states that every bridgeless cubic graph has 5 perfect matchings such that each edge is contained in at least one of them. In this paper, we show that Berge Conjecture holds for two classes of cubic graphs, cubic graphs…
We demonstrate that a tree-based theory for various dynamical processes yields extremely accurate results for several networks with high levels of clustering. We find that such a theory works well as long as the mean intervertex distance…
Several results about the union-closed sets conjecture are presented.
We prove a fix point theorem for monoids of self-embeddings of trees. As a corollary, we obtain a result by Laflamme, Pouzet and Sauer that a tree either contains a subdivided binary tree as a subtree or has a vertex, and edge, an end or…
We make two improvements upon Joyce's gluing theorems of for compact special Lagrangian submanifolds with isolated conical singularities. Firstly, we get rid of a few technical hypotheses of them. Secondly, we replace another hypothesis by…
Inspired by the spread of information in social networks and graph-theoretic processes such as Firefighting and graph cleaning, Bonato, Janssen and Roshanbin introduced in 2016 the burning number $b(G)$ of any finite graph $G$. They…
The classical Berge-Fulkerson conjecture states that any bridgeless cubic graph $G$ admits a list of six perfect matchings such that each edge of $G$ belongs to two of the perfect matchings from the list. In this short note, we discuss two…
The Hodge conjecture is shown to hold for rationally connected fivefolds, or more generally for fivefolds for which the base of the maximal rationally connected fibration is at most 3 dimensional.
We carry out a gluing construction for collapsing warped-QAC (quasi-asymptotically-conical) Calabi-Yau manifolds in $\CC^{n+2}, n\geq 2$. This gluing theorem verifies a conjecture by Yang Li in \cite{li2019gluing} on the behavior of the…
We study algebras on which the Berenstein-Zelevinsky conjecture is true. In particular, we prove that this conjecture is true "up to localization".
The Gy\'arf\'as tree packing conjecture asserts that any set of trees with $2,3, ..., k$ vertices has an (edge-disjoint) packing into the complete graph on $k$ vertices. Gy\'arf\'as and Lehel proved that the conjecture holds in some special…