Research
Research
Research
Research
806+ open-access research outputs.
For a graph $G$, let $f_o(G)$ denote the maximum order of an induced subgraph of $G$ all of whose vertices have odd degree, and let $\chi(G)$ denote the chromatic number of $G$. Scott (CPC, 1992) prov…
In this paper, we use a variety of classical and new research methods for ternary exponential Diophantine equations and extensive use of computer calculations to study the conjecture of R. Scott and R…
This paper proposes a strong second-order two-step explicit/implicit technique with spectral orthogonal basis Galerkin finite element method for solving a two-dimensional Gray-Scott model subject to a…
For a set of $n$ points $V \subseteq \mathbb{R}$ let $G(V, p)$ be the random graph on $V$ where each possible edge is present independently with probability $p$. We call a subset $U \subseteq V$ {\emp…
We introduce the Thue--Morse transform, a transform on binary sequences defined through their evil and odious numbers, namely the positions of $0$'s and $1$'s, respectively, and prove that its iterate…
In this paper, we discuss topological aspects of the space of valuations $\mathbb{V}$ and the valuative tree $\mathcal{T}(v,\Lambda)$. We present a relation between the weak tree topology and the Scot…
We consider a two-component semilinear reaction-diffusion system in a bounded spatial domain $\Omega$ over a time interval $(0,T)$, which governs the water density $u(x,t)$ and the vegetation biomass …
We study the following focusing intercritical nonlinear Schr\"odinger equation with partial harmonic confinement: \begin{equation*} \begin{cases} i\partial_t u+\Delta_{z}u-y^2 u =- |u|^{\alpha}u,\qu…
A graph is chordal if it contains no induced cycle of length four or more. While finite chordal graphs are precisely those admitting tree-decompositions into cliques, this fails for infinite graphs. W…
Disaster relief operations often take place under uncertainty regarding the extent of damage across locations. In this paper, we study the delivery of relief aid in the aftermath of disasters when del…
This is the first paper that provides a systematic treatment of the $r$-dimensional PTE problem in additive number theory, abbreviated by PTE$_r$, through its connection with combinatorial design theo…
Let $V$ be a finite-dimensional real vector space. A collection $\mathcal{P} = \{(A_i,B_i)\}_{i=1}^m$ of pairs of subspaces of $V$ is called a skew Bollob\'as system if $\dim(A_i\cap B_i)=0$ for each …
Given a labelled tournament on $[n]$, \emph{inverting} a vertex subset $X$ means reversing every edge with both endpoints in $X$. Alon, Powierski, Savery, Scott, and Wilmer~\cite{AlonPowierskiSaverySc…
Let $V \subset \mathbb{R}$ be a finite set with $|V| = n $ and suppose we are given each pairwise distance independently with probability $p$. We show that if $p = (1+\epsilon)/n$, for some fixed $\ep…
One measure of the complexity of a first-order theory, and similarly a type, is the complexity of the formulas required to axiomatize it. We say a theory is bounded if there is an axiomatization invol…
We study symplectic forms on hypersurface algebroids. These are a broad generalization of the $b^{k}$-Poisson structures studied extensively by Miranda, Scott, and collaborators, and their geometry is…
For a graph $G$, $\chi(G)$ denotes the chromatic number of $G$ and $\omega(G)$ denotes the size of the largest clique in $G$. A hereditary class of graphs is called $\chi$-bounded if there is a functi…
Scott and Karp gave an analysis which provides a level-by-level equivalence between global similarity between two structures and local commonality in terms of sharing particular invariants. Scott and …
We discuss the back and forth technique in the context of presheaf model theory. The essence of the back and forth technique lies in showing the relationship between various hierarchies which calibrat…
Meyniel's conjecture states that $n$-vertex connected graphs have cop number $O(\sqrt{n})$. The current best known upper bound is $n/2^{(1-o(1))\sqrt{\log n}}$, proved independently by Lu and Peng (20…
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