数学最新文献

{"title":"Research problems from the 1st Chinese–Southeasteuropean conference on discrete mathematics and applications","authors":"Vedran Krčadinac ,&nbsp;Shenggui Zhang ,&nbsp;Liming Xiong ,&nbsp;Dragan Stevanović","doi":"10.1016/j.dam.2025.02.037","DOIUrl":"10.1016/j.dam.2025.02.037","url":null,"abstract":"<div><div>This is a collection of open problems related to/presented at the 1st Chinese–Southeasteuropean conference on discrete mathematics and applications that was held at Serbian Academy of Sciences and Arts in Belgrade, Serbia, from June 9–14, 2024.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"371 ","pages":"Pages 99-104"},"PeriodicalIF":1.0,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143739099","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Weak degeneracy of the square of K4-minor free graphs","authors":"Jing Ye ,&nbsp;Jiani Zou ,&nbsp;Miaomiao Han","doi":"10.1016/j.amc.2025.129439","DOIUrl":"10.1016/j.amc.2025.129439","url":null,"abstract":"<div><div>A graph <em>G</em> is called weakly <em>f</em>-degenerate with respect to a function <em>f</em> from <span><math><mi>V</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span> to the non-negative integers, if every vertex of <em>G</em> can be successively removed through a series of valid Delete and DeleteSave operations. The weak degeneracy <span><math><mi>w</mi><mi>d</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span> is defined as the smallest integer <em>d</em> for which <em>G</em> is weakly <em>d</em>-degenerate, where <em>d</em> is a constant function. It was demonstrated that one plus the weak degeneracy can act as an upper bound for list-chromatic number and DP-chromatic number. Let <span><math><mi>κ</mi><mo>(</mo><msup><mrow><mi>G</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo><mo>=</mo><mi>Δ</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>+</mo><mn>2</mn></math></span> if <span><math><mn>2</mn><mo>≤</mo><mi>Δ</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>≤</mo><mn>3</mn></math></span>, and <span><math><mi>κ</mi><mo>(</mo><msup><mrow><mi>G</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo><mo>=</mo><mo>⌊</mo><mfrac><mrow><mn>3</mn><mi>Δ</mi><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mrow><mn>2</mn></mrow></mfrac><mo>⌋</mo></math></span> if <span><math><mi>Δ</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>≥</mo><mn>4</mn></math></span>. In this paper, we prove that for every <span><math><msub><mrow><mi>K</mi></mrow><mrow><mn>4</mn></mrow></msub></math></span>-minor free graph <em>G</em>, <span><math><mi>w</mi><mi>d</mi><mo>(</mo><msup><mrow><mi>G</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo><mo>≤</mo><mi>κ</mi><mo>(</mo><msup><mrow><mi>G</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></math></span>, which implies that <span><math><msup><mrow><mi>G</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> is <span><math><mo>(</mo><mi>κ</mi><mo>(</mo><msup><mrow><mi>G</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo><mo>+</mo><mn>1</mn><mo>)</mo></math></span>-choosable and <span><math><mo>(</mo><mi>κ</mi><mo>(</mo><msup><mrow><mi>G</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo><mo>+</mo><mn>1</mn><mo>)</mo></math></span>-DP-colorable. This work generalizes the result obtained by Lih et al. in [Discrete Mathematics, 269 (2003), 303-309] and Hetherington et al. in [Discrete Mathematics, 308 (2008), 4037-4043].</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"500 ","pages":"Article 129439"},"PeriodicalIF":3.5,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143738712","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Aubin–Nitsche-type estimates for space-time FOSLS for parabolic PDEs","authors":"Thomas Führer ,&nbsp;Gregor Gantner","doi":"10.1016/j.camwa.2025.03.017","DOIUrl":"10.1016/j.camwa.2025.03.017","url":null,"abstract":"<div><div>We develop Aubin–Nitsche-type estimates for recently proposed first-order system least-squares finite element methods (FOSLS) for the heat equation. Under certain assumptions, which are satisfied if the spatial domain is convex and the heat source and initial datum are sufficiently smooth, we prove that the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> error of approximations of the scalar field variable converges at a higher rate than the overall error. Furthermore, a higher-order conservation property is shown. In addition, we discuss quasi-optimality in weaker norms. Numerical experiments confirm our theoretical findings.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"186 ","pages":"Pages 155-170"},"PeriodicalIF":2.9,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143739854","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Edge-disjoint cycles with the same vertex set","authors":"Debsoumya Chakraborti ,&nbsp;Oliver Janzer ,&nbsp;Abhishek Methuku ,&nbsp;Richard Montgomery","doi":"10.1016/j.aim.2025.110228","DOIUrl":"10.1016/j.aim.2025.110228","url":null,"abstract":"<div><div>In 1975, Erdős asked for the maximum number of edges that an <em>n</em>-vertex graph can have if it does not contain two edge-disjoint cycles on the same vertex set. It is known that Turán-type results can be used to prove an upper bound of <span><math><msup><mrow><mi>n</mi></mrow><mrow><mn>3</mn><mo>/</mo><mn>2</mn><mo>+</mo><mi>o</mi><mo>(</mo><mn>1</mn><mo>)</mo></mrow></msup></math></span>. However, this approach cannot give an upper bound better than <span><math><mi>Ω</mi><mo>(</mo><msup><mrow><mi>n</mi></mrow><mrow><mn>3</mn><mo>/</mo><mn>2</mn></mrow></msup><mo>)</mo></math></span>. We show that there is an absolute constant <em>t</em> and some constant <span><math><mi>c</mi><mo>=</mo><mi>c</mi><mo>(</mo><mi>k</mi><mo>)</mo></math></span> such that for each <span><math><mi>k</mi><mo>≥</mo><mn>2</mn></math></span>, every <em>n</em>-vertex graph with at least <span><math><mi>c</mi><mi>n</mi><msup><mrow><mo>(</mo><mi>log</mi><mo>⁡</mo><mi>n</mi><mo>)</mo></mrow><mrow><mi>t</mi></mrow></msup></math></span> edges contains <em>k</em> pairwise edge-disjoint cycles with the same vertex set, resolving this old problem in a strong form up to a polylogarithmic factor. The well-known construction of Pyber, Rödl and Szemerédi of graphs without 4-regular subgraphs shows that there are <em>n</em>-vertex graphs with <span><math><mi>Ω</mi><mo>(</mo><mi>n</mi><mi>log</mi><mo>⁡</mo><mi>log</mi><mo>⁡</mo><mi>n</mi><mo>)</mo></math></span> edges which do not contain two cycles with the same vertex set, so the polylogarithmic term in our result cannot be completely removed.</div><div>Our proof combines a variety of techniques including sublinear expanders, absorption and a novel tool for regularisation, which is of independent interest. Among other applications, this tool can be used to regularise an expander while still preserving certain key expansion properties.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"469 ","pages":"Article 110228"},"PeriodicalIF":1.5,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143739280","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Multifractal analysis of temperature in Europe: Climate change effect","authors":"Borko Stosic ,&nbsp;Tatijana Stosic ,&nbsp;Ivana Tošić ,&nbsp;Vladimir Djurdjević","doi":"10.1016/j.chaos.2025.116386","DOIUrl":"10.1016/j.chaos.2025.116386","url":null,"abstract":"<div><div>We investigated multifractality of temporal series of daily mean air temperature anomalies over the entire European continent by applying the method Multifractal detrended fluctuation analysis (MFDFA) on high resolution E-OBSv26.0e dataset. The spatial resolution is 0.1⁰ which corresponds to 120,866 grid cells, and the time span of daily temperature series is from 1961 to 2020, which permits to compare two climate periods (1961–1990 and 1991–2020) and evaluate the impact of climate change. For each grid cell and each of the two periods we calculated the multifractal spectrum <span><math><mi>f</mi><mfenced><mi>α</mi></mfenced></math></span> which contains the information about specific properties of temperature series: persistence (described by the position of the maximum of the spectrum <span><math><msub><mi>α</mi><mn>0</mn></msub></math></span>), strength of multifractality (described by the spectrum width <span><math><mi>W</mi></math></span>) and the contribution of large/small fluctuations (described by the spectrum skew parameter <span><math><mi>r</mi><mo>)</mo><mo>.</mo></math></span>We found that in both periods temperature series exhibit properties of a multifractal process, with persistent long-term correlations (<span><math><msub><mi>α</mi><mn>0</mn></msub><mo>&gt;</mo><mn>0.5</mn><mo>)</mo><mspace></mspace></math></span>and the dominance of scaling of small fluctuations (<span><math><mi>r</mi><mo>&gt;</mo><mn>0</mn></math></span>). The spatial distribution of multifractal parameters exhibits a distinct gradient during the first period. The parameter <span><math><msub><mi>α</mi><mn>0</mn></msub></math></span> (persistence) increases from west to east and from south to north. In contrast, <span><math><mi>W</mi></math></span> (strength of multifractality) decreases from south to north in regions outside Eastern Europe, whereas it increases from south to north within Eastern Europe. In the second period, the area with stronger multifractality (higher <span><math><mi>W</mi></math></span> values) of temperature anomalies expanded significantly in Eastern Europe. The spatially averaged value and the range of the width <em>W</em> of the multifractal spectrum increased in the second period following the increase of the mean daily temperature. These results reveal the impact of climate change on multifractal properties of air temperature.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"196 ","pages":"Article 116386"},"PeriodicalIF":5.3,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143738970","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Relative cubulation of relative strict hyperbolization","authors":"Jean-François Lafont,&nbsp;Lorenzo Ruffoni","doi":"10.1112/jlms.70093","DOIUrl":"https://doi.org/10.1112/jlms.70093","url":null,"abstract":"<p>We prove that many relatively hyperbolic groups obtained by relative strict hyperbolization admit a cocompact action on a <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>CAT</mo>\u0000 <mo>(</mo>\u0000 <mn>0</mn>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$operatorname{CAT}(0)$</annotation>\u0000 </semantics></math> cubical complex. Under suitable assumptions on the peripheral subgroups, these groups are residually finite and even virtually special. We include some applications to the theory of manifolds, such as the construction of new non-positively curved Riemannian manifolds with residually finite fundamental group, and the existence of non-triangulable aspherical manifolds with virtually special fundamental group.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 4","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70093","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143741249","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Modeling and experimental circuit implementation of fractional single-transistor chaotic oscillators","authors":"Longxiang Fu ,&nbsp;Wanting Zhu ,&nbsp;Bo Yu ,&nbsp;Yaoyao Zhang ,&nbsp;Pedro Antonio Valdes-Sosa ,&nbsp;Chunbiao Li ,&nbsp;Leonardo Ricci ,&nbsp;Mattia Frasca ,&nbsp;Ludovico Minati","doi":"10.1016/j.amc.2025.129438","DOIUrl":"10.1016/j.amc.2025.129438","url":null,"abstract":"<div><div>This study presents the first experimental realization of a single-transistor fractional chaotic oscillator, obtained by extending a minimalistic integer-order circuit by systematically transforming its reactive components, namely two inductors and a capacitor, into fractional elements. Starting from the Grünwald-Letnikov definition and using a string structure finite-order approximation for implementation, the dynamics are studied over a range of fractional orders. Results from equation models, circuit simulations, and experimental measurements are juxtaposed, yielding broadly consistent results. The introduction of fractional elements is found to have profound effects on the chaotic dynamics, influencing oscillation amplitude, spectral flatness, and bifurcation characteristics. In particular, inspection of the resulting Poincaré sections reveals a gradual distortion of the interplay between the relaxation and resonance aspects of the circuit dynamics with decreasing fractional order. While less generative than other manipulations, such as inserting fractal resonators, the ability to introduce fractional components into elementary nonlinear oscillator circuits provides a new, highly versatile, and compact physical tool. Potential applications include modeling electronically real-world phenomena endowed with considerable memory and nonlocality, such as neural activity and viscoelasticity.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"500 ","pages":"Article 129438"},"PeriodicalIF":3.5,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143738713","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Gibbs measures for geodesic flow on CAT(-1) spaces","authors":"Caleb Dilsavor ,&nbsp;Daniel J. Thompson","doi":"10.1016/j.aim.2025.110231","DOIUrl":"10.1016/j.aim.2025.110231","url":null,"abstract":"<div><div>For a proper geodesically complete CAT(-1) space equipped with a discrete non-elementary action, and a bounded continuous potential with the Bowen property, we construct weighted quasi-conformal Patterson densities and use them to build a Gibbs measure on the space of geodesic lines. Our construction yields a Gibbs measure with local product structure for any potential in this class, which includes bounded Hölder continuous potentials. Furthermore, if the Gibbs measure is finite, then we prove that it is the unique equilibrium state. In contrast to previous results in this direction, we do not require any condition that the potential must take the same value on two geodesic lines which share a common segment.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"469 ","pages":"Article 110231"},"PeriodicalIF":1.5,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143739282","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Hardy's uncertainty principle for Schrödinger equations with quadratic Hamiltonians","authors":"Elena Cordero,&nbsp;Gianluca Giacchi,&nbsp;Eugenia Malinnikova","doi":"10.1112/jlms.70134","DOIUrl":"https://doi.org/10.1112/jlms.70134","url":null,"abstract":"<p>Hardy's uncertainty principle is a classical result in harmonic analysis, stating that a function in <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mi>L</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mi>d</mi>\u0000 </msup>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$L^2(mathbb {R}^d)$</annotation>\u0000 </semantics></math> and its Fourier transform cannot both decay arbitrarily fast at infinity. In this paper, we extend this principle to the propagators of Schrödinger equations with quadratic Hamiltonians, known in the literature as metaplectic operators. These operators generalize the Fourier transform and have captured significant attention in recent years due to their wide-ranging applications in time-frequency analysis, quantum harmonic analysis, signal processing, and various other fields. However, the involved structure of these operators requires careful analysis, and most results obtained so far concern special propagators that can basically be reduced to rescaled Fourier transforms. The main contributions of this work are threefold: (1) we extend Hardy's uncertainty principle, covering all propagators of Schrödinger equations with quadratic Hamiltonians, (2) we provide concrete examples, such as fractional Fourier transforms, which arise when considering anisotropic harmonic oscillators, (3) we suggest Gaussian decay conditions in certain directions only, which are related to the geometry of the corresponding Hamiltonian flow.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 4","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70134","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143741250","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The oriented diameter of a bridgeless graph with the given path Pk","authors":"Ruijuan Li,&nbsp;Shufeng Chen","doi":"10.1016/j.disc.2025.114509","DOIUrl":"10.1016/j.disc.2025.114509","url":null,"abstract":"<div><div>Let <span><math><mi>G</mi><mo>=</mo><mo>(</mo><mi>V</mi><mo>,</mo><mi>E</mi><mo>)</mo></math></span> be a bridgeless undirected graph. The oriented diameter of <em>G</em> is the minimum diameter of any strongly connected orientation of <em>G</em>. Dankelmann, Guo and Surmacs [J. Graph Theory, 88 (2018), 5-17] showed that every bridgeless graph <em>G</em> of order <em>n</em> has an oriented diameter at most <span><math><mi>n</mi><mo>−</mo><mi>Δ</mi><mo>+</mo><mn>3</mn></math></span>, where Δ is the maximum degree of <em>G</em>. By defining <span><math><msub><mrow><mi>N</mi></mrow><mrow><mi>G</mi></mrow></msub><mo>(</mo><mi>H</mi><mo>)</mo><mo>=</mo><msub><mrow><mo>⋃</mo></mrow><mrow><mi>v</mi><mo>∈</mo><mi>V</mi><mo>(</mo><mi>H</mi><mo>)</mo></mrow></msub><msub><mrow><mi>N</mi></mrow><mrow><mi>G</mi></mrow></msub><mo>(</mo><mi>v</mi><mo>)</mo><mo>∖</mo><mi>V</mi><mo>(</mo><mi>H</mi><mo>)</mo></math></span> for every subgraph <em>H</em> of <em>G</em>, they proved that for an edge <em>e</em>, <em>G</em> has an orientation of diameter at most <span><math><mi>n</mi><mo>−</mo><mo>|</mo><msub><mrow><mi>N</mi></mrow><mrow><mi>G</mi></mrow></msub><mo>(</mo><mi>e</mi><mo>)</mo><mo>|</mo><mo>+</mo><mn>5</mn></math></span>. In this paper, we generalize the above-mentioned results by substituting a vertex or an edge <em>e</em> by a given path <span><math><msub><mrow><mi>P</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>=</mo><msub><mrow><mi>v</mi></mrow><mrow><mn>1</mn></mrow></msub><msub><mrow><mi>v</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>⋯</mo><msub><mrow><mi>v</mi></mrow><mrow><mi>k</mi></mrow></msub></math></span> in <em>G</em>. We first give an algorithm to cover <span><math><msub><mrow><mi>P</mi></mrow><mrow><mi>k</mi></mrow></msub></math></span> with some specific cycles, and then prove the upper bound <span><math><mi>n</mi><mo>−</mo><mo>|</mo><msub><mrow><mi>N</mi></mrow><mrow><mi>G</mi></mrow></msub><mo>(</mo><msub><mrow><mi>P</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>)</mo><mo>|</mo><mo>+</mo><mn>2</mn><mo>⌊</mo><mfrac><mrow><mi>k</mi></mrow><mrow><mn>2</mn></mrow></mfrac><mo>⌋</mo><mo>+</mo><mn>3</mn></math></span> on the oriented diameter. We provide examples to show that our bound is sharp.</div></div>","PeriodicalId":50572,"journal":{"name":"Discrete Mathematics","volume":"348 9","pages":"Article 114509"},"PeriodicalIF":0.7,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143737820","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}