相关论文: Outermost boundaries for star-connected components…

Consider a connected graph $G$ and let $T$ be a spanning tree of $G$. Every edge $e \in G-T$ induces a cycle in $T \cup \{e\}$. The intersection of two distinct such cycles is the set of edges of $T$ that belong to both cycles. The MSTCI…

Percolation in systems made up of randomly placed impermeable grains is often examined in the context of system spanning clusters of connected solids forming above a relatively low critical grain density $\rho_{c1}$ or networks of…

If the universe is finite and smaller than the distance to the surface of last scatter, then the signature of the topology of the universe is writ on the microwave background sky. Previous efforts to search for this topology have focused on…

One of the most well-known classical results for site percolation on the square lattice is the equation p_c + p_c^* = 1. In words, this equation means that for all values different from p_c of the parameter p the following holds: Either…

We propose an evolutionary path for prestellar cores on the radius-mass diagram, which is analogous to stellar evolutionary paths on the Hertzsprung-Russell Diagram. Using James Clerk Maxwell Telescope (JCMT) observations of L1688 in the…

We consider homological edge percolation on a sequence $(\mathcal{G}_t)_t$ of finite graphs covered by an infinite (quasi)transitive graph $\mathcal{H}$, and weakly convergent to $\mathcal{H}$. Namely, we use the covering maps to classify…

Start with a graph with a subset of vertices called {\it the border}. A particle released from the origin performs a random walk on the graph until it comes to the immediate neighbourhood of the border, at which point it joins this subset…

Bound states in the continuum (BICs) are polarization singularities in momentum space whose topological charges (TCs) govern advanced light-matter interactions. While lattice symmetry protects the existence of robust BICs at the…

Recently, optical bound states in continuum in various passive photonic crystals have been identified and similar structures incorporated with optical gain have been reported to exhibit lasing. However, no explicit control over the type of…

We introduce a new oriented evolving graph model inspired by biological networks. A node is added at each time step and is connected to the rest of the graph by random oriented edges emerging from older nodes. This leads to a statistical…

We consider the Boolean model on $\R^d$. We prove some equivalences between subcritical percolation properties. Let us introduce some notations to state one of these equivalences. Let $C$ denote the connected component of the origin in the…

Consider balls $\Lambda_n$ of growing volumes in the $d$-dimensional hierarchical lattice, and place edges independently between each pair of vertices $x\neq y\in\Lambda_n$ with probability $1-\exp(-\beta J(x, y) )$ where $J(x, y) \asymp \|…

The $g$-component edge connectivity $c\lambda_g(G)$ of a non-complete graph $G$ is the minimum number of edges whose deletion results in a graph with at least $g$ components. In this paper, we determine the component edge connectivity of…

We introduce a new approach to disordered two-dimensional Ising models based on the extension of the combinatorial solution to randomized supercells. Applying it to the site-diluted Ising model on the square lattice, we resolve the full…

We determine which connected surfaces can be partitioned into topological circles. There are exactly seven such surfaces up to homeomorphism: those of finite type, of Euler characteristic zero, and with compact boundary components. As a…

Hyperbolic structures are obtained by tiling a hyperbolic surface with negative Gaussian curvature. These structures generally exhibit two percolation transitions: a system-wide connection can be established at a certain occupation…

Jets from young stellar objects provide insight into the workings of the beating heart at the centre of star forming cores. In some cases, multiple pulsed outflows are detected such as the atomic and molecular jets from a proposed binary…

A star edge-coloring of a graph $G$ is a proper edge-coloring without bichromatic paths or cycles of length four. The smallest integer $k$ such that $G$ admits a star edge-coloring with $k$ colors is the star chromatic index of $G$. In the…

A set S is independent in a graph G if no two vertices from S are adjacent. By core(G) we mean the intersection of all maximum independent sets. The independence number alpha(G) is the cardinality of a maximum independent set, while mu(G)…

Gy\'arf\'as famously showed that in every $r$-coloring of the edges of the complete graph $K_n$, there is a monochromatic connected component with at least $\frac{n}{r-1}$ vertices. A recent line of study by Conlon, Tyomkyn, and the second…