相关论文: Cancellative hypergraphs and Steiner triple system…
The 3-decomposition conjecture is wide open. It asserts that every finite connected cubic graph can be decomposed into a spanning tree, a disjoint union of cycles, and a matching. We show that every such decomposition is derived from a…
Motivated by the counting results for color-critical subgraphs by Mubayi [Adv. Math., 2010], we study the phenomenon behind Mubayi's theorem from a spectral perspective and start up this problem with the fundamental case of triangles. We…
We conjecture that the balanced complete bipartite graph $K_{\lfloor n/2 \rfloor,\lceil n/2 \rceil}$ contains more cycles than any other $n$-vertex triangle-free graph, and we make some progress toward proving this. We give equivalent…
For a closed system to equilibrate from a given initial condition there must exist an equilibrium state with the energy equal to the initial one. Equilibrium states of a strongly coupled gauge theory with a gravitational holographic dual…
The main result of this paper is that, if $\Gamma$ is a connected 4-valent $G$-arc-transitive graph and $v$ is a vertex of $\Gamma$, then either $\Gamma$ is one of a well understood infinite family of graphs, or $|G_v|\leq 2^43^6$ or…
Rabern recently proved that any graph with omega >= (3/4)(Delta+1) contains a stable set meeting all maximum cliques. We strengthen this result, proving that such a stable set exists for any graph with omega > (2/3)(Delta+1). This is tight,…
Let $n,k,s$ be three integers such that $k\geq 2$ and $n\geq s\geq 1$. Let $H$ be a $k$-partite $k$-uniform hypergraph with $n$ vertices in each class. Aharoni (2017) showed that if $e(H)>(s-1)n^{k-1}$, then $H$ has a matching of size $s$.…
Given an STS(v), we ask if there is a permutation of the points of the design such that no $\ell$ consecutive points in this permutation contain a block of the design. Results are obtained in the cases $\ell = 3,4$.
We give a complete description of the set of triples (a,b,c) of real numbers with the following property. There exists a constant K such that a n_3 + b n_2 + c n_1 - K is a lower bound for the matching number of every connected subcubic…
In this paper, we study perturbation of Hilbert-Schmidt frames under structured modifications, where the perturbation takes the form of replacing finitely or infinitely many frame elements. We establish explicit criteria under which the…
Supersymmetric states in M-theory are mapped after compactification to perturbatively non-supersymmetric states in type IIA string theory, with the supersymmetric parts being encoded in the non-perturbative section of the string theory. An…
Turaev's shadow can be seen locally as the Stein factorization of a stable map. In this paper, we define the notion of stable map complexity for a compact orientable 3-manifold bounded by (possibly empty) tori counting, with some weights,…
A design is said to be $f$-pyramidal when it has an automorphism group which fixes $f$ points and acts sharply transitively on all the others. The problem of establishing the set of values of $v$ for which there exists an $f$-pyramidal…
We prove a version of the strong Taylor's conjecture for stable graphs: if $G$ is a stable graph whose chromatic number is strictly greater than $\beth_2(\aleph_0)$ then $G$ contains all finite subgraphs of Sh$_n(\omega)$ and thus has…
A Berge-$K_4$ in a triple system is a configuration with four vertices $v_1,v_2,v_3,v_4$ and six distinct triples $\{e_{ij}: 1\le i< j \le 4\}$ such that $\{v_i,v_j\}\subset e_{ij}$ for every $1\le i<j\le 4$. We denote by $\cal{B}$ the set…
We discuss a theoretical framework to define an optimal sub-grid closure for shell models of turbulence. The closure is based on the ansatz that consecutive shell multipliers are short-range correlated, following the third hypothesis of…
In this short note we prove a hierarchical stability result that applies to hybrid dynamical systems satisfying the hybrid basic conditions of (Goebel et al., 2012). In particular, we establish sufficient conditions for uniform asymptotic…
The entanglement of quantum systems can produce a variety of nonclassical effects that have practical applications in quantum information science. One example of this is nonlocal dispersion cancellation, in which the effects of dispersion…
It is known that hyperbolic non\-autonomous linear delay differential equations in a finite dimensional space are Hyers--Ulam stable and hence shadowable. The converse result is available only in the special case of autonomous and periodic…
We study the mediation of supersymmetry breaking in string compactifications whose moduli are stabilized by nonperturbative effects. We begin with a critical review of arguments for sequestering in supergravity and in string theory. We then…