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Acyclic Edge Coloring of 1-planar Graphs without 4-cycles 无 4 循环的 1 平面图的无循环边着色
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-01-03 DOI: 10.1007/s10255-024-1101-z
Wei-fan Wang, Yi-qiao Wang, Wan-shun Yang
{"title":"Acyclic Edge Coloring of 1-planar Graphs without 4-cycles","authors":"Wei-fan Wang,&nbsp;Yi-qiao Wang,&nbsp;Wan-shun Yang","doi":"10.1007/s10255-024-1101-z","DOIUrl":"10.1007/s10255-024-1101-z","url":null,"abstract":"<div><p>An acyclic edge coloring of a graph <i>G</i> is a proper edge coloring such that there are no bichromatic cycles in <i>G</i>. The acyclic chromatic index <span>(cal{X}_{alpha}^{prime}(G))</span> of <i>G</i> is the smallest <i>k</i> such that <i>G</i> has an acyclic edge coloring using <i>k</i> colors. It was conjectured that every simple graph <i>G</i> with maximum degree Δ has <span>(cal{X}_{alpha}^{prime}(G)leDelta+2)</span>. A 1-planar graph is a graph that can be drawn in the plane so that each edge is crossed by at most one other edge. In this paper, we show that every 1-planar graph <i>G</i> without 4-cycles has <span>(cal{X}_{alpha}^{prime}(G)leDelta+22)</span>.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"40 1","pages":"35 - 44"},"PeriodicalIF":0.9,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139092405","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Clustering for Bivariate Functional Data 二元函数数据聚类
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-01-03 DOI: 10.1007/s10255-024-1116-5
Shi-yun Cao, Yan-qiu Zhou, Yan-ling Wan, Tao Zhang
{"title":"Clustering for Bivariate Functional Data","authors":"Shi-yun Cao,&nbsp;Yan-qiu Zhou,&nbsp;Yan-ling Wan,&nbsp;Tao Zhang","doi":"10.1007/s10255-024-1116-5","DOIUrl":"10.1007/s10255-024-1116-5","url":null,"abstract":"<div><p>In this paper, we consider the clustering of bivariate functional data where each random surface consists of a set of curves recorded repeatedly for each subject. The <i>k</i>-centres surface clustering method based on marginal functional principal component analysis is proposed for the bivariate functional data, and a novel clustering criterion is presented where both the random surface and its partial derivative function in two directions are considered. In addition, we also consider two other clustering methods, <i>k</i>-centres surface clustering methods based on product functional principal component analysis or double functional principal component analysis. Simulation results indicate that the proposed methods have a nice performance in terms of both the correct classification rate and the adjusted rand index. The approaches are further illustrated through empirical analysis of human mortality data.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"40 3","pages":"613 - 629"},"PeriodicalIF":0.9,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139092088","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Perturbed Compound Poisson Risk Model with Proportional Investment 带投资比例的扰动复合泊松风险模型
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-01-03 DOI: 10.1007/s10255-024-1102-y
Nai-dan Deng, Chun-wei Wang, Jia-en Xu
{"title":"The Perturbed Compound Poisson Risk Model with Proportional Investment","authors":"Nai-dan Deng,&nbsp;Chun-wei Wang,&nbsp;Jia-en Xu","doi":"10.1007/s10255-024-1102-y","DOIUrl":"10.1007/s10255-024-1102-y","url":null,"abstract":"<div><p>In this paper, the insurance company considers venture capital and risk-free investment in a constant proportion. The surplus process is perturbed by diffusion. At first, the integro-differential equations satisfied by the expected discounted dividend payments and the Gerber-Shiu function are derived. Then, the approximate solutions of the integro-differential equations are obtained through the sinc method. Finally, the numerical examples are given when the claim sizes follow different distributions. Furthermore, the errors between the explicit solution and the numerical solution are discussed in a special case.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"40 1","pages":"109 - 128"},"PeriodicalIF":0.9,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139092403","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Neighbor Sum Distinguishing Total Choosability of Planar Graphs with Maximum Degree at Least 10 最大阶数至少为 10 的平面图的邻域和区分总可选择性
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-01-03 DOI: 10.1007/s10255-024-1110-y
Dong-han Zhang, You Lu, Sheng-gui Zhang, Li Zhang
{"title":"Neighbor Sum Distinguishing Total Choosability of Planar Graphs with Maximum Degree at Least 10","authors":"Dong-han Zhang,&nbsp;You Lu,&nbsp;Sheng-gui Zhang,&nbsp;Li Zhang","doi":"10.1007/s10255-024-1110-y","DOIUrl":"10.1007/s10255-024-1110-y","url":null,"abstract":"<div><p>A neighbor sum distinguishing (NSD) total coloring <i>ϕ</i> of <i>G</i> is a proper total coloring of <i>G</i> such that <span>(sumlimits_{z in {E_G}(u) cup {u}} {phi (z) ne} sumlimits_{z in {E_G}(v) cup {v}} {phi (z)} )</span> for each edge <i>uv</i> ∈ <i>E</i>(<i>G</i>), where <i>EG</i>(<i>u</i>) is the set of edges incident with a vertex <i>u</i>. In 2015, Pilśniak and Woźniak conjectured that every graph with maximum degree Δ has an NSD total (Δ + 3)-coloring. Recently, Yang et al. proved that the conjecture holds for planar graphs with Δ ≥ 10, and Qu et al. proved that the list version of the conjecture also holds for planar graphs with Δ ≥ 13. In this paper, we improve their results and prove that the list version of the conjecture holds for planar graphs with Δ ≥ 10.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"40 1","pages":"211 - 224"},"PeriodicalIF":0.9,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139096732","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Geometric Constraints for Global Regularity of 3D Shear Thickening Fluids 三维剪切增稠流体全局规则性的几何约束
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-01-03 DOI: 10.1007/s10255-024-1114-7
Jia-qi Yang
{"title":"Geometric Constraints for Global Regularity of 3D Shear Thickening Fluids","authors":"Jia-qi Yang","doi":"10.1007/s10255-024-1114-7","DOIUrl":"10.1007/s10255-024-1114-7","url":null,"abstract":"<div><p>We consider the relation between the direction of the vorticity and the global regularity of 3D shear thickening fluids. It is showed that a weak solution to the non-Newtonian incompressible fluid in the whole space is strong if the direction of the vorticity is <span>({{11 - 5p} over 2})</span>-Hölder continuous with respect to the space variables when <span>(2 &lt; p &lt; {{11} over 5})</span>.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"40 1","pages":"205 - 210"},"PeriodicalIF":0.9,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139092145","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the Difference Between the Skew-rank of an Oriented Graph and the Rank of Its Underlying Graph 论定向图的倾斜秩与其底层图的秩之间的差异
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-01-03 DOI: 10.1007/s10255-024-1103-x
Jia-min Zhu, Bo-jun Yuan, Yi Wang
{"title":"On the Difference Between the Skew-rank of an Oriented Graph and the Rank of Its Underlying Graph","authors":"Jia-min Zhu,&nbsp;Bo-jun Yuan,&nbsp;Yi Wang","doi":"10.1007/s10255-024-1103-x","DOIUrl":"10.1007/s10255-024-1103-x","url":null,"abstract":"<div><p>Let <i>G</i> be a simple graph and <i>G</i><sup><i>σ</i></sup> be the oriented graph with <i>G</i> as its underlying graph and orientation <i>σ</i>. The rank of the adjacency matrix of <i>G</i> is called the rank of <i>G</i> and is denoted by <i>r</i>(<i>G</i>). The rank of the skew-adjacency matrix of <i>G</i><sup><i>σ</i></sup> is called the skew-rank of <i>G</i><sup><i>σ</i></sup> and is denoted by <i>sr</i>(<i>G</i><sup><i>σ</i></sup>). Let <i>V</i>(<i>G</i>) be the vertex set and <i>E</i>(<i>G</i>) be the edge set of <i>G</i>. The cyclomatic number of <i>G</i>, denoted by <i>c</i>(<i>G</i>), is equal to ∣<i>E</i>(<i>G</i>)∣ − ∣<i>V</i>(<i>G</i>)∣+ <i>ω</i>(<i>G</i>), where <i>ω</i>(<i>G</i>) is the number of the components of <i>G</i>. It is proved for any oriented graph <i>G</i><sup><i>σ</i></sup> that −2<i>c</i>(<i>G</i>) ⩽ sr(<i>G</i><sup><i>σ</i></sup>) − <i>r</i>(<i>G</i>) ⩽ 2<i>c</i>(<i>G</i>). In this paper, we prove that there is no oriented graph <i>G</i><sup><i>σ</i></sup> with <i>sr</i>(<i>G</i><sup><i>σ</i></sup>) − <i>r</i>(<i>G</i>) = 2<i>c</i>(<i>G</i>)−1, and in addition, there are in nitely many oriented graphs <i>G</i><sup><i>σ</i></sup> with connected underlying graphs such that <i>c</i>(<i>G</i>) = <i>k</i> and <i>sr</i>(<i>G</i><sup><i>σ</i></sup>)−<i>r</i>(<i>G</i>) = 2<i>c</i>(<i>G</i>)−ℓ for every integers <i>k</i>, ℓ satisfying 0 ⩽ ℓ ⩽ 4<i>k</i> and ℓ≠ 1.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"40 1","pages":"129 - 136"},"PeriodicalIF":0.9,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139092094","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Pseudomonotonicity of Nonlinear Transformations on Euclidean Jordan Algebras 欧几里得约旦代数上非线性变换的假单调性
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-01-03 DOI: 10.1007/s10255-024-1108-5
Yuan-Min Li
{"title":"Pseudomonotonicity of Nonlinear Transformations on Euclidean Jordan Algebras","authors":"Yuan-Min Li","doi":"10.1007/s10255-024-1108-5","DOIUrl":"10.1007/s10255-024-1108-5","url":null,"abstract":"<div><p>In this paper, we have introduced the concepts of pseudomonotonicity properties for nonlinear transformations defined on Euclidean Jordan algebras. The implications between this property and other P-properties have been studied. More importantly, we have solved the solvability problem of the nonlinear pseudomonotone complementarity problems over symmetric cones.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"40 1","pages":"192 - 204"},"PeriodicalIF":0.9,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139092399","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Global Zero-relaxation Limit Problem of the Electro-diffusion Model Arising in Electro-Hydrodynamics 电流体力学中出现的电扩散模型的全局零松弛极限问题
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-01-03 DOI: 10.1007/s10255-024-1119-2
Ming-hua Yang, Si-ming Huang, Jin-yi Sun
{"title":"Global Zero-relaxation Limit Problem of the Electro-diffusion Model Arising in Electro-Hydrodynamics","authors":"Ming-hua Yang,&nbsp;Si-ming Huang,&nbsp;Jin-yi Sun","doi":"10.1007/s10255-024-1119-2","DOIUrl":"10.1007/s10255-024-1119-2","url":null,"abstract":"<div><p>In this paper, we study a global zero-relaxation limit problem of the electro-diffusion model arising in electro-hydrodynamics which is the coupled Planck-Nernst-Poisson and Navier-Stokes equations. That is, the paper deals with a singular limit problem of </p><div><div><span>$$left{ begin{gathered}\u0000begin{array}{*{20}{c}}\u0000{u_t^varepsilon+ {u^varepsilon } cdot nabla {u^varepsilon } - Delta {u^varepsilon } + nabla {P^varepsilon } = Delta {phi ^varepsilon }nabla {phi ^varepsilon },}&amp;{in{text{ }}{mathbb{R}^3} times (0,infty )} \u0000{nablacdot {u^varepsilon } = 0,}&amp;{in{text{ }}{mathbb{R}^3} times (0,infty )} \u0000end{array} hfill begin{array}{*{20}{c}}\u0000{n_t^varepsilon+ {u^varepsilon } cdot nabla {n^varepsilon } - Delta {n^varepsilon } =- nablacdot ({n^varepsilon }nabla {phi ^varepsilon }),}&amp;{in{text{ }}{mathbb{R}^3} times (0,infty )} \u0000{c_t^varepsilon+ {u^varepsilon } cdot nabla {c^varepsilon } - Delta {c^varepsilon } = nablacdot ({c^varepsilon }nabla {phi ^varepsilon }),}&amp;{in{text{ }}{mathbb{R}^3} times (0,infty )} \u0000end{array} hfill begin{array}{*{20}{c}}\u0000{{varepsilon ^{ - 1}}phi _t^varepsilon= Delta {phi ^varepsilon } - {n^varepsilon } + {c^varepsilon },}&amp;{in{text{ }}{mathbb{R}^3} times (0,infty )} \u0000{({u^varepsilon },{n^varepsilon },{c^varepsilon },{phi ^varepsilon })left| {_{t = 0 = ({u_0},{n_0},{c_0},{phi _0})},} right.}&amp;{in{text{ }}{mathbb{R}^3}} \u0000end{array} hfill \u0000end{gathered}right.$$</span></div></div><p> involving with a positive, large parameter <i>ϵ</i>. The present work show a case that (<i>u</i><sup><i>ϵ</i></sup>, <i>n</i><sup><i>ϵ</i></sup>, <i>c</i><sup><i>ϵ</i></sup>) stabilizes to (<i>u</i><sup>∞</sup>, <i>n</i><sup>∞</sup>, <i>c</i><sup>∞</sup>):= (<i>u, n, c</i>) uniformly with respect to the time variable as <i>ϵ</i> → + ∞ with respect to the strong topology in a certain Fourier-Herz space.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"40 1","pages":"241 - 268"},"PeriodicalIF":0.9,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139092412","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Multicolored Bipartite Ramsey Numbers of Large Cycles 大循环的多色二方拉姆齐数
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2023-12-29 DOI: 10.1007/s10255-024-1118-3
Shao-qiang Liu, Yue-jian Peng
{"title":"Multicolored Bipartite Ramsey Numbers of Large Cycles","authors":"Shao-qiang Liu,&nbsp;Yue-jian Peng","doi":"10.1007/s10255-024-1118-3","DOIUrl":"10.1007/s10255-024-1118-3","url":null,"abstract":"<div><p>For an integer <i>r</i> ≥ 2 and bipartite graphs <i>H</i><sub><i>i</i></sub>, where 1≤ <i>i</i> ≤ <i>r</i> the bipartite Ramsey number <i>br</i>(<i>H</i><sub>1</sub>, <i>H</i><sub>2</sub>, …, <i>H</i><sub><i>r</i></sub>) is the minimum integer <i>N</i> such that any <i>r</i>-edge coloring of the complete bipartite graph <i>K</i><sub><i>N,N</i></sub> contains a monochromatic subgraph isomorphic to <i>H</i><sub><i>i</i></sub> in color <i>i</i> for some 1 ≤ <i>i</i> ≤ <i>r</i>. We show that if <span>(r ge 3,{alpha _1},{alpha _2} &gt; 0,{alpha _{j + 2}} ge [(j + 2)! - 1]sumlimits_{i = 1}^{j + 1} {{alpha _i}} )</span> for <i>j</i> = 1, 2, …, <i>r</i> −2, then <span>(br({C_{2leftlfloor {{alpha _1},n} rightrfloor }},{C_{2leftlfloor {{alpha _2},n} rightrfloor }}, cdots ,{C_{2leftlfloor {{alpha _r},n} rightrfloor }}) = (sumlimits_{j = 1}^r {{alpha _j} + o(1))n} )</span>.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"40 2","pages":"347 - 357"},"PeriodicalIF":0.9,"publicationDate":"2023-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139062661","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Ramsey Numbers of Trees Versus Multiple Copies of Books 拉姆齐树的数量与多本图书的数量
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2023-12-29 DOI: 10.1007/s10255-024-1117-4
Xiao-bing Guo, Si-nan Hu, Yue-jian Peng
{"title":"Ramsey Numbers of Trees Versus Multiple Copies of Books","authors":"Xiao-bing Guo,&nbsp;Si-nan Hu,&nbsp;Yue-jian Peng","doi":"10.1007/s10255-024-1117-4","DOIUrl":"10.1007/s10255-024-1117-4","url":null,"abstract":"<div><p>Given two graphs <i>G</i> and <i>H</i>, the Ramsey number <i>R</i>(<i>G,H</i>) is the minimum integer <i>N</i> such that any two-coloring of the edges of <i>K</i><sub><i>N</i></sub> in red or blue yields a red <i>G</i> or a blue <i>H</i>. Let <i>v</i>(<i>G</i>) be the number of vertices of <i>G</i> and <i>χ</i>(<i>G</i>) be the chromatic number of <i>G</i>. Let <i>s</i>(<i>G</i>) denote the chromatic surplus of <i>G</i>, the number of vertices in a minimum color class among all proper <i>χ</i>(<i>G</i>)-colorings of <i>G</i>. Burr showed that <span>(R(G,H) ge (v(G) - 1)(chi (H) - 1) + s(H))</span> if <i>G</i> is connected and <span>(v(G) ge s(H))</span>. A connected graph <i>G</i> is <i>H</i>-good if <span>(R(G,H) = (v(G) - 1)(chi (H) - 1) + s(H))</span>. Let <i>tH</i> denote the disjoint union of <i>t</i> copies of graph <i>H</i>, and let <span>(G vee H)</span> denote the join of <i>G</i> and <i>H</i>. Denote a complete graph on <i>n</i> vertices by <i>K</i><sub><i>n</i></sub>, and a tree on <i>n</i> vertices by <i>T</i><sub><i>n</i></sub>. Denote a book with <i>n</i> pages by <i>B</i><sub><i>n</i></sub>, i.e., the join <span>({K_2} vee overline {{K_n}} )</span>. Erdős, Faudree, Rousseau and Schelp proved that <i>T</i><sub><i>n</i></sub> is <i>B</i><sub><i>m</i></sub>-good if <span>(n ge 3m - 3)</span>. In this paper, we obtain the exact Ramsey number of <i>T</i><sub><i>n</i></sub> versus 2<i>B</i><sub>2</sub>- Our result implies that <i>T</i><sub><i>n</i></sub> is 2<i>B</i><sub>2</sub>-good if <i>n</i> ≥ 5.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"40 3","pages":"600 - 612"},"PeriodicalIF":0.9,"publicationDate":"2023-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139062851","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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