arXiv subjects

Jan Jedelský

Publications and source records attributed to Jan Jedelský.

11 recordsLinked to original sources

arXiv2026

k-Planar and Fan-Crossing Drawings and Transductions of Embeddable Graphs

We introduce, for every surface $Σ$, a two-way connection between definability of a graph class $\mathcal C$ by FO transductions (first-order logical transformations) of the graphs embeddable in $Σ$ and a certain variant of fan-crossing drawings of the graphs from $\mathcal C$ in $Σ$. If $\mathcal C$ is additionally of bounded maximum degree, then the restriction on drawings of the graphs from $\mathcal C$ in $Σ$ is simply to have a bounded number of crossings per edge (such as being $k$-planar for fixed~$k$ if $Σ$ is the plane). For graph classes, this connection allows us to derive non-transducibility results from the nonexistence of the said drawings and, conversely, from the nonexistence of a transduction to derive nonexistence of the said drawings. One example of such reasoning is as follows; since the class of 3D-grids is not transducible from the class of planar graphs, we can conclude that the class of 3D-grids is not $k$-planar for any fixed~$k$. On the other hand, the fact that the class of 3D-grids is not $k$-planar for any fixed~$k$ is known also via other means, and this conversely implies that the class of 3D-grids is not transducible from the class of planar graphs. We hope that this connection will help to draw a path to a possible proof that not all toroidal graphs are transducible from planar graphs. The result is based on a recent characterization of weakly sparse FO transductions of classes of bounded expansion by [Gajarský, Gładkowski, Jedelský, Pilipczuk and Toruńczyk, arXiv:2505.15655].

cs.CG↗

arXiv2026

Hereditary Graph Product Structure and $\cal H$-clique-width

We introduce H-clique-width, a new structural measure of graphs that aims to provide a hereditary analogue of the traditional graph product structure. The definition naturally generalises the ordinary clique-width concept. As a result, for a class H of graphs (such as the class of paths), the H-clique-width of a graph G equals the least integer t such that G is isomorphic to an induced subgraph of the strong product of a graph from H and a graph of clique-width t. We study basic properties of H-clique-width and compare it to other established structural parameters of graphs. Notably, we prove that the celebrated Planar graph product structure theorem by Dujmovic et al., and related graph product structure results, can all be formulated with the induced subgraph containment relation. In particular, every planar graph is isomorphic to an induced subgraph of the strong product of a path and a graph of tree-width 39.

math.CO↗

arXiv2026

Measuring Depth of Matroids

Motivated by recently discovered connections between matroid depth measures and block-structured integer programming [ICALP 2020, 2022], we undertake a systematic study of recursive depth parameters for matrices and matroids, aiming to unify recently introduced and scattered concepts. We propose a general framework that naturally yields eight different depth measures for matroids, prove their fundamental properties and relationships, and relate them to two established notions in the field: matroid branch-depth and a newly introduced natural depth counterpart of matroid tree-width. In particular, we show that six of our eight measures are mutually functionally inequivalent, and among these, one is functionally equivalent to matroid branch-depth and another to matroid tree-depth. Importantly, we also prove that these depth measures coincide on matroids and on matrices over any field, which is (somehow surprisingly) not a trivial task. Finally, we provide a comparison between the matroid parameters and classical depth measures of graphs.

math.CO↗

arXiv2026

On first-order model checking parameterized by the number of variables

The first-order (FO) model checking problem asks, given an FO sentence $ϕ$ and a graph $G$, whether $G$ is a model of $ϕ$. This problem is known to be $\mathsf{AW[*]}$-hard when parameterized by the quantifier rank of the formula. A classical algorithm decides this problem in XP-time parameterized by the number of variables in the formula. Due to $\mathsf{AW[*]}$-hardness, it is natural to ask about the complexity of the problem when restricted to some well-behaved class of graphs. There are many results describing graph classes $\mathcal{C}$ such that the FO model checking problem restricted to $\mathcal{C}$ admits an $\mathsf{FPT}$-time algorithm when parameterized by the quantifier rank of the formula. Parameterization by the quantifier rank is significantly more restrictive than parameterization by the number of variables. We investigate the graph classes $\mathcal{C}$ for which the FO model checking problem restricted to $\mathcal{C}$ admits an $\mathsf{FPT}$-time algorithm when parameterized by the number of variables in the formula. We characterize these classes in the monotone setting, and prove a slightly weaker result in the hereditary setting.

cs.LO↗

arXiv2025

Spatio-temporal analysis of sprays by using Phase Doppler Anemometry data

Spray characterization often relies on empirical formulas, statistical distributions, and derived quantities. Deterministic spray behavior originates from physics-governed mechanisms of atomization, \emph{e.g.}, nozzle geometry, boundary conditions, and hydrodynamic instabilities. Due to the stochastic nature of the atomization process, which originates from turbulence, chaotic perturbations, and droplet--droplet interactions, the temporal characteristics of dynamic behavior are seldom investigated. The combination of these processes leads to droplet clustering, which is a spatio-temporal behavior that is the focus of the current paper for an airblast atomizer. The measurement data by Phase Doppler Anemometry include droplet size, velocity, and arrival time. Firstly, the theoretical and experimental interparticle time distributions are compared using a $χ^2$ hypothesis test, which concluded multimodality. Secondly, \emph{k}-means clustering is applied to determine droplet clusters, whose number was determined by gap statistics. The above analysis was performed using an extensive database of various measurement positions, atomizing pressures, liquid preheating temperatures, and liquid types. It was found that cluster formation affects approximately 30\% of the droplets in a single data set. In conclusion, the unsteadiness in the central region is caused by clustering, while it is caused by mixing and droplet entrainment in the spray periphery. The centroids and the number of cluster values depend on the atomizing pressure and the spray position, and are independent of the liquid temperature. The dynamical behavior of the clusters is compared by their droplet size and velocity distributions, showing no significant difference, suggesting that unsteady spray modeling is necessary if temporal characteristics are critical.

physics.flu-dyn↗

arXiv2025

Transductions of Graph Classes Admitting Product Structure

In a quest to thoroughly understand the first-order transduction hierarchy of hereditary graph classes, some questions in particular stand out; such as, what properties hold for graph classes that are first-order transductions of planar graphs (and of similar classes)? When addressing this (so-far wide open) question, we turn to the concept of a product structure - being a subgraph of the strong product of a path and a graph of bounded tree-width, introduced by Dujmovic et al. [JACM 2020]. Namely, we prove that any graph class which is a first-order transduction of a class admitting such product structure, up to perturbations also meets a structural description generalizing the concept of a product structure in a dense hereditary way - the latter concept being introduced just recently by Hlineny and Jedelsky under the name of H-clique-width [MFCS 2024]. Using this characterization, we show that the class of the 3D grids, as well as a class of certain modifications of 2D grids, are not first-order transducible from classes admitting a product structure, and in particular not from the class of planar graphs.

cs.LO↗

arXiv2025

First-order transducibility among classes of sparse graphs

We prove several negative results about first-order transducibility for classes of sparse graphs: - for every $t \in \mathbb{N}$, the class of graphs of treewidth at most $t+1$ is not transducible from the class of graphs of treewidth at most $t$; - for every $t \in \mathbb{N}$, the class of graphs with Hadwiger number at most $t+2$ is not transducible from the class of graphs with Hadwiger number at most $t$; and - the class of graphs of treewidth at most $4$ is not transducible from the class of planar graphs. These results are obtained by combining the known upper and lower bounds on the weak coloring numbers of the considered graph classes with the following two new observations: - If a weakly sparse graph class $\mathscr D$ is transducible from a class $\mathscr C$ of bounded expansion, then for some $k \in \mathbb{N}$, every graph $G \in \mathscr D$ is a $k$-congested depth-$k$ minor of a graph $H^\circ$ obtained from some $H\in \mathscr C$ by adding a universal vertex. - The operations of adding a universal vertex and of taking $k$-congested depth-$k$ minors, for a fixed $k$, preserve the degree of the distance-$d$ weak coloring number of a graph class, understood as a polynomial in $d$.

cs.LO↗

arXiv2024

Statistical evaluation and Phase Doppler Anemometry data processing of rotary atomization

Rotary atomization is used in a wide variety of fields, exploiting the external control option of the spray while no high-pressure fluid is needed. Most papers on rotary atomization deal with liquid jet breakup, while external spray characteristics are rarely evaluated; this is performed currently. The water spray was measured by a two-component Phase Doppler Anemometer. The optical setup requires a special measurement chamber to avoid spray deposition on the optical components. Therefore, the first goal was to find a proper filter that enables the removal of biased droplets by secondary flows. Since most droplets have a similar radial-to-tangential velocity ratio at each measurement point, i.e., scattering around a line, this was the first component of the best filter. The second component was the need for a positive radial velocity component. This filter efficiently removed droplets originating from alternative processes, increasing the R2 of the line fit. The physical soundness of this filter was checked by evaluating the effect of filtering on the angle of the velocity components of each droplet at a given measurement point. The proposed filter efficiently detected recirculation, a secondary effect of the measurement setup with less regular data set shapes. Finally, the slope and intercept values of the fitted lines were evaluated and presented. The mean of the former followed the same trend irrespective of the rotational speed and the mass flow rate; it was principally dependent on the radial distance from the atomizer. The intercept showed a regular but less universal behavior.

physics.flu-dyn↗

arXiv2023

Twin-width of Planar Graphs is at most 8, and some Related Bounds

Twin-width is a structural width parameter introduced by Bonnet, Kim, Thomassé and Watrigant [FOCS 2020], and has interesting applications in the areas of logic on graphs and in parameterized algorithmics. Very briefly, the essence of twin-width is in a gradual reduction (a contraction sequence) of the given graph down to a single vertex while maintaining limited difference of neighbourhoods of the vertices, and it can be seen as widely generalizing several other traditional structural parameters. While for many natural graph classes it is known that their twin-width is bounded, published upper bounds on the twin-width in non-trivial cases are very often "astronomically large". We focus on planar graphs, which are known to have bounded twin-width already since the introduction of it, but it took some time for the first explicit "non-astronomical" upper bounds to come. Namely, in the order of preprint appearance, it was the bound of at most 183 by Jacob and Pilipczuk [arXiv, January 2022], and 583 by Bonnet, Kwon and Wood [arXiv, February 2022]. Subsequent arXiv manuscripts in 2022 improved the bound down to 37 (Bekos et al.), 11 and 9 (both by Hliněný). We further elaborate on the approach used in the latter manuscripts, proving that the twin-width of every planar graph is at most 8, and construct a witnessing contraction sequence in linear time. Note that the currently best lower-bound planar example is of twin-width 7, by Král and Lamaison [arXiv, September 2022]. We also prove small explicit upper bounds on the twin-width of bipartite planar and 1-planar graphs (6 and 16), and of map graphs (38). The common denominator of all these results is the use of a novel specially crafted recursive decomposition of planar graphs, which may be found useful also in other areas.

math.CO↗

arXiv2022

Twin-width and Transductions of Proper k-Mixed-Thin Graphs

The new graph parameter twin-width, introduced by Bonnet, Kim, Thomass e and Watrigant in 2020, allows for an FPT algorithm for testing all FO properties of graphs. This makes classes of efficiently bounded twin-width attractive from the algorithmic point of view. In particular, classes of efficiently bounded twin-width include proper interval graphs, and (as digraphs) posets of width k. Inspired by an existing generalization of interval graphs into so-called k-thin graphs, we define a new class of proper k-mixed-thin graphs which largely generalizes proper interval graphs. We prove that proper k-mixed-thin graphs have twin-width linear in k, and that a slight subclass of k-mixed-thin graphs is transduction-equivalent to posets of width k' such that there is a quadratic-polynomial relation between k and k'. In addition to that, we also give an abstract overview of the so-called red potential method which we use to prove our twin-width bounds.

math.CO↗

arXiv2022

Numerical modeling of distributed combustion without air dilution in a novel ultra-low emission turbulent swirl burner

Distributed combustion, often associated with the low-oxygen condition, offers ultra-low NOX emission. However, it was recently achieved without combustion air dilution or internal flue gas recirculation, using a distinct approach called Mixture Temperature-Controlled combustion. Here, the fuel-air stream is cooled at the inlet to delay ignition and hence foster homogeneous mixture formation. The aim of this numerical study aims to understand the operation of this combustion concept better and present a robust framework for distributed combustion modeling in a parameter range where such operation was not predicted before by any existing theory. Further, liquid fuel combustion was evaluated that brings additional complexity. Four operating conditions were presented at which distributed combustion was observed. The reacting flow was modeled by Flamelet-Generated Manifold, based on a detailed n-dodecane mechanism. The Zimont turbulent flame speed model was used with significantly reduced coefficients to achieve distributed combustion. The droplets of airblast atomization were tracked in a Lagrangian frame. The numerical results were validated by Schlieren images and acoustic spectra. It was concluded that the reactant dilution ratio remained below 0.25 through the combustion chamber, revealing that the homogeneous fuel-air mixture is the principal reason for excellent flame stability and ultra-low NOX emission without significant internal recirculation. The potential applications of these results are boilers, furnaces, and gas turbines.

physics.flu-dyn↗