Research
Research
Research
Research
215+ open-access research outputs.
We determine the full persistence probability distribution for a non-Markovian stochastic process, motivated by first-passage questions arising in interacting spin systems and allied systems. We show …
The longstanding conjecture of Halin characterizing the existence of normal spanning trees in infinite graphs has been recently proved by Max Pitz [3]. A critical step in the proof involves the constr…
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…
Total coloring of a graph is a coloring of its vertices and edges such that adjacent or incident elements receive distinct colors. Total coloring conjecture (stipulating that the total chromatic numbe…
A $t$-tone $k$-coloring of a graph $G$ assigns a set of $t$ distinct colors from $\{1, \dots, k\}$ to each vertex so that vertices at distance $d$ share fewer than $d$ common colors. The $t$-tone chro…
Assume $\kappa = \kappa^{< \kappa}$ (usually $\aleph_0$ or an inaccessible). We shall deal with iterated forcings preserving ${}^{\kappa>}{\rm Ord}$ and not collapsing cardinals along a linear order…
We review a certain problem on covering triangles in the plane. Equivalently, it can be viewed as a family of 'isobilliard' inequalities in convex shapes, and as a special case of Viterbo's conjecture…
The Internet of Battlefield Things (IoBT) relies on heterogeneous, bandwidth-constrained, and intermittently connected tactical networks that face rapidly evolving cyber threats. In this setting, intr…
Motivated by frequency assignment problems in wireless broadcast networks, Goddard, Hedetniemi, Hedetniemi, Harris, and Rall introduced the notion of $S$-packing coloring in 2008. Given a non-decreasi…
Halin characterised the chordal locally finite graphs as those that admit a tree-decomposition into cliques. We show that these tree-decompositions can be chosen to be canonical, that is, so that they…
We study the existence and cardinality of universal families for classes of rayless graphs. It is known, by a result of Diestel, Halin, and Vogler, that the class of countable rayless graphs does not …
We investigate the critical temperature of a relativistic Bose-Einstein condensate of charged bosons driven by rotation in a parallel magnetic field [Y. Liu and I. Zahed, Phys. Rev. Lett. 120, 032001 …
Given a graph or multigraph $G$, let $\chi'_{trans}(G)$ denote the minimum integer $n$ such that any proper $\chi'(G)$--edge coloring of $G$ can be transformed into any other proper $\chi'(G)$--edge c…
The star chromatic index of a graph $G$, denoted by $\chi'_{st}(G) $, is the minimum number of colors needed to properly color the edges of $G$ such that no path or cycle of length four is bi-colored.…
We investigate a class of nonlocal gradients featuring distinct homogeneities at zero and infinity. We establish a representation formula for such doubly homogeneous operators and derive associated So…
In this paper, we introduce super-minimally $k$-connected graphs, those $k$-connected graphs in which no proper subgraph is $k$-connected. For $k$ greater than or equal to three, this class lies stric…
Halin conjectured that a graph has a normal spanning tree if and only if every minor of it has countable colouring number. This has recently been proven by the second author. In this paper, we stren…
Symplectic capacities are invariants in symplectic geometry that are used to obstruct symplectic embeddings. From a certain symplectic capacity, the Ekeland-Hofer-Zehnder capacity, one can construct t…
We prove that the edge-end space of an infinite graph is metrizable if and only if it is first-countable. This strengthens a recent result by Aurichi, Magalhaes Jr.\ and Real (2024). Our central gra…
We prove a coarse version of Halin's Grid Theorem: Every one-ended, locally finite graph that contains the disjoint union of infinitely many rays as an asymptotic minor also contains the half-grid as …
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