Related papers: Some Exact Results for Spanning Trees on Lattices
Alon and Wormald showed that any graph with minimum degree d contains a spanning star forest in which every connected component is of size at least \Omega((d/\log d)^{1/3}). They asked if any connected graph with minimum degree at least d…
Inspired by the seminal works of Khuller et al. (STOC 1994) and Chan (SoCG 2003) we study the bottleneck version of the Euclidean bounded-degree spanning tree problem. A bottleneck spanning tree is a spanning tree whose largest edge-length…
Branched polymers can be classified into two categories that obey the different formulae: \begin{equation} \nu= \begin{cases} \hspace{1mm}\displaystyle\frac{2(1+\nu_{0})}{d+2} & \hspace{3mm}\mbox{for polymers…
We study the set of visible lattice points in multidimensional hypercubes. The problems we investigate mix together geometric, probabilistic and number theoretic tones. For example, we prove that almost all self-visible triangles with…
A smooth path of rearrangement from the body-centered cubic (bcc) to the face-centered cubic (fcc) lattice is obtained by introducing a single parameter to cuboidal lattice vectors. As a result, we obtain analytical expressions in terms of…
We study a new bi-Lipschitz invariant \lambda(M) of a metric space M; its finiteness means that Lipschitz functions on an arbitrary subset of M can be linearly extended to functions on M whose Lipschitz constants are enlarged by a factor…
We perform a tree-level O(a) improvement of two-dimensional N=(2,2) supersymmetric Yang-Mills theory on the lattice, motivated by the fast convergence in numerical simulations. The improvement respects an exact supersymmetry Q which is…
We study the relation between the minimal spanning tree (MST) on many random points and the "near-minimal" tree which is optimal subject to the constraint that a proportion $\delta$ of its edges must be different from those of the MST.…
We examine the issue of the cosmological constant in the $many$ $inflating$ branes scenario, extending on two recent models by I.Oda and Randall-Sundrum. The exact solution in a closed form is found in the slow roll approximation of the…
We present results on the QCD equation of state, obtained with two different improved dynamical staggered fermion actions and almost physical quark masses. Lattice cut-off effect are discussed in detail as results for three different…
A tree is called k-ended tree if it has at most k leaves, where a leaf is a vertex of degree one. In this paper we prove that every 3-regular connected graph with n vertices such that n is greater than 8 has spanning sub tree with at most…
The celebrated result of Koml\'os, S\'ark\"ozy, and Szemer\'edi states that for any $\varepsilon>0$, there exists $0<c<1$, such that for all sufficiently large $n$, every $n$-vertex graph $G$ with $\delta(G)\geq(1/2+\varepsilon)n$ contains…
The Flatness theorem states that the maximum lattice width ${\rm Flt}(d)$ of a $d$-dimensional lattice-free convex set is finite. It is the key ingredient for Lenstra's algorithm for integer programming in fixed dimension, and much work has…
We examine the exponentially improved asymptotic expansion of the Lerch zeta function $L(\lambda,a,s)=\sum_{n=1}^\infty \exp (2\pi ni\lambda)/(n+a)^s$ for large complex values of $a$, with $\lambda$ and $s$ regarded as parameters. It is…
We present a link-by-link rule-based method for constructing all members of the ensemble of spanning trees for any recursively generated, finitely articulated graph, such as the DGM net. The recursions allow for many large-scale properties…
We study gradient models on the lattice $\mathbb{Z}^d$ with non-convex interactions. These Gibbs fields (lattice models with continuous spin) emerge in various branches of physics and mathematics. In quantum field theory they appear as…
In this article, we extend Moon's classic formula for counting spanning trees in complete graphs containing a fixed spanning forest to complete bipartite graphs. Let $(X,Y)$ be the bipartition of the complete bipartite graph $K_{m,n}$ with…
We calculate the mean and almost-sure leading order behaviour of the high frequency asymptotics of the eigenvalue counting function associated with the natural Dirichlet form on $\alpha$-stable trees, which lead in turn to short-time heat…
In this paper we give an exact analytical expression for the number of spanning trees of an infinite family of outerplanar, small-world and self-similar graphs. This number is an important graph invariant related to different topological…
We study numerically three-dimensional Z(N) lattice gauge theories at finite temperature, for N = 5, 6, 8, 12, 13 and 20 on lattices with temporal extension $N_t$ = 2, 4, 8. For each model, we locate phase transition points and determine…