Journal of Graph Theory最新文献

英文中文

Independent Domination Number of Planar Triangulations 平面三角剖分的独立支配数

IF 1 3区数学 Q2 MATHEMATICS

Journal of Graph Theory

Pub Date : 2025-07-17 DOI: 10.1002/jgt.23285

P. Francis, Abraham M. Illickan, Lijo M. Jose, Deepak Rajendraprasad

We show that every planar triangulation on $� � � � � n � � �$ vertices has a maximal independent set of size at most $� � � � � n � � / � � 3 � � �$ . This affirms a conjecture by Botler, Fernandes, and Gutiérrez (Electron. J. Comb., 2024) based on an open question of Goddard and Henning (Appl. Math. Comput., 2020). Since a maximal independent set is a special type of dominating set (independent dominating set), this is a structural strengthening of a major result by Matheson and Tarjan (Eur. J. Comb., 1996) that every triangulated disc has a dominating set of size at most $� � � � � n � � / � � 3 � � �$ , but restricted to triangulations.

我们证明了在n个顶点上的每个平面三角剖分都有一个最大独立集，其大小最多为n / 3。这证实了Botler、Fernandes和gutisamurez （Electron）的一个猜想。j .梳子。， 2024)基于戈达德和亨宁（苹果公司）的一个开放问题。数学。第一版。, 2020)。由于极大独立集是一种特殊类型的支配集（独立支配集），这是Matheson和Tarjan （Eur）的一个主要结果的结构强化。j .梳子。（1996），每个三角化圆盘都有一个最大为n / 3的支配集，但仅限于三角化。

{"title":"Independent Domination Number of Planar Triangulations","authors":"P. Francis, Abraham M. Illickan, Lijo M. Jose, Deepak Rajendraprasad","doi":"10.1002/jgt.23285","DOIUrl":"https://doi.org/10.1002/jgt.23285","url":null,"abstract":"<div>\u0000 \u0000 We show that every planar triangulation on <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> vertices has a maximal independent set of size at most <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>n</mi>\u0000 \u0000 <mo>/</mo>\u0000 \u0000 <mn>3</mn>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>. This affirms a conjecture by Botler, Fernandes, and Gutiérrez (Electron. J. Comb., 2024) based on an open question of Goddard and Henning (Appl. Math. Comput., 2020). Since a maximal independent set is a special type of dominating set (independent dominating set), this is a structural strengthening of a major result by Matheson and Tarjan (Eur. J. Comb., 1996) that every triangulated disc has a dominating set of size at most <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>n</mi>\u0000 \u0000 <mo>/</mo>\u0000 \u0000 <mn>3</mn>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>, but restricted to triangulations.\u0000 </div>","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"110 4","pages":"426-430"},"PeriodicalIF":1.0,"publicationDate":"2025-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145272803","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}

引用次数: 0

A Spectral Erdős–Faudree–Rousseau Theorem A谱Erdős-Faudree-Rousseau定理

IF 1 3区数学 Q2 MATHEMATICS

Journal of Graph Theory

Pub Date : 2025-07-16 DOI: 10.1002/jgt.23280

Yongtao Li, Lihua Feng, Yuejian Peng

A well-known theorem of Mantel states that every $� � � � � n � � �$ -vertex graph with more than $� � � � � � ⌊ � � � �^{n � � 2 �} � � ∕ � � 4 � � � ⌋ � � � �$ edges contains a triangle. An interesting problem in extremal graph theory studies the minimum number of edges contained in triangles among graphs with a prescribed number of vertices and edges. Erdős, Faudree, and Rousseau (1992) showed that a graph on $� � � � � n � � �$ vertices with more than $� � � � � � ⌊ � � � �^{n � � 2 �} � � ∕ � � 4 � � � ⌋ � � � �$ edges contains at least $� � � � � 2 � � � ⌊ � � � n � � ∕ � � 2 � � � ⌋ � � � + � �$

一个著名的曼特尔定理指出，每一个大于⌊n2的n顶点图∕4⌋边包含一个三角形。极值图论中一个有趣的问题是研究给定顶点和边数的图中三角形所包含的最小边数。Faudree Erdő年代,和Rousseau（1992）展示了在数组中有n个大于n2的顶点的图∕4⌋边至少包含2个数组N∕2⌋+ 1条三角形边。这样的边称为三角形边。在本文中，我们提出了Erdős， Faudree和Rousseau的结果的光谱版本。利用过饱和稳定性和光谱技术，我们证明了每一个具有λ (G)≥⌊n 2∕4⌋至少包含2⌊n∕2⌋−1条三角形边，除非G是平衡完全二部图。本文的方法有一些有趣的应用。首先，过饱和稳定性可以用来重新审视Erdős关于图的书大小的猜想，该猜想最初由Edwards（未发表）证明，并且由Khadžiivanov和Nikiforov（1979）独立证明。其次，当我们禁止友谊图作为子结构时，我们的方法可以改善谱极值图的n阶界。我们放弃了要求n足够大的条件，这是cioabei et al.（2020）使用三角形去除引理研究的。第三，该方法可用于推导奇环的经典稳定性，并给出了更简洁的参数界。最后，过饱和稳定性可以应用于处理计数三角形上的谱图问题，这是Ning和Zhai（2023）最近研究的。

{"title":"A Spectral Erdős–Faudree–Rousseau Theorem","authors":"Yongtao Li, Lihua Feng, Yuejian Peng","doi":"10.1002/jgt.23280","DOIUrl":"https://doi.org/10.1002/jgt.23280","url":null,"abstract":"<div>\u0000 \u0000 A well-known theorem of Mantel states that every <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>-vertex graph with more than <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mrow>\u0000 <mo>⌊</mo>\u0000 \u0000 <mrow>\u0000 <msup>\u0000 <mi>n</mi>\u0000 \u0000 <mn>2</mn>\u0000 </msup>\u0000 \u0000 <mo>∕</mo>\u0000 \u0000 <mn>4</mn>\u0000 </mrow>\u0000 \u0000 <mo>⌋</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> edges contains a triangle. An interesting problem in extremal graph theory studies the minimum number of edges contained in triangles among graphs with a prescribed number of vertices and edges. Erdős, Faudree, and Rousseau (1992) showed that a graph on <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> vertices with more than <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mrow>\u0000 <mo>⌊</mo>\u0000 \u0000 <mrow>\u0000 <msup>\u0000 <mi>n</mi>\u0000 \u0000 <mn>2</mn>\u0000 </msup>\u0000 \u0000 <mo>∕</mo>\u0000 \u0000 <mn>4</mn>\u0000 </mrow>\u0000 \u0000 <mo>⌋</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> edges contains at least <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mn>2</mn>\u0000 \u0000 <mrow>\u0000 <mo>⌊</mo>\u0000 \u0000 <mrow>\u0000 <mi>n</mi>\u0000 \u0000 <mo>∕</mo>\u0000 \u0000 <mn>2</mn>\u0000 </mrow>\u0000 \u0000 <mo>⌋</mo>\u0000 </mrow>\u0000 \u0000 <mo>+</mo>\u0000 \u0000 ","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"110 4","pages":"408-425"},"PeriodicalIF":1.0,"publicationDate":"2025-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145272905","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}

引用次数: 0

Counterexamples Regarding Linked and Lean Tree-Decompositions of Infinite Graphs 关于无限图的链接和精益树分解的反例

IF 1 3区数学 Q2 MATHEMATICS

Journal of Graph Theory

Pub Date : 2025-07-15 DOI: 10.1002/jgt.23279

Sandra Albrechtsen, Raphael W. Jacobs, Paul Knappe, Max Pitz

Kříž and Thomas showed that every (finite or infinite) graph of tree-width

� � �                     � � k �                        � \in �                        � N � � �

admits a lean tree-decomposition of width

� � �                     � � k � � �

. We discuss a number of counterexamples demonstrating the limits of possible generalisations of their result to arbitrary infinite tree-width. In particular, we construct a locally finite, planar, connected graph that has no lean tree-decomposition.

Kříž和Thomas证明了树宽度k∈N的每一个（有限或无限）图都允许宽度为k的精益树分解。我们讨论了一些反例，证明了它们的结果可能推广到任意无限树宽的极限。特别地，我们构造了一个局部有限的平面连通图，它没有精益树分解。

{"title":"Counterexamples Regarding Linked and Lean Tree-Decompositions of Infinite Graphs","authors":"Sandra Albrechtsen, Raphael W. Jacobs, Paul Knappe, Max Pitz","doi":"10.1002/jgt.23279","DOIUrl":"https://doi.org/10.1002/jgt.23279","url":null,"abstract":"Kříž and Thomas showed that every (finite or infinite) graph of tree-width <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>k</mi>\u0000 \u0000 <mo>∈</mo>\u0000 \u0000 <mi>N</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> admits a lean tree-decomposition of width <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>k</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>. We discuss a number of counterexamples demonstrating the limits of possible generalisations of their result to arbitrary infinite tree-width. In particular, we construct a locally finite, planar, connected graph that has no lean tree-decomposition.","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"110 4","pages":"398-407"},"PeriodicalIF":1.0,"publicationDate":"2025-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/jgt.23279","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145273041","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Face Sizes and the Connectivity of the Dual 脸的大小和双连通性

IF 1 3区数学 Q2 MATHEMATICS

Journal of Graph Theory

Pub Date : 2025-07-13 DOI: 10.1002/jgt.23277

Gunnar Brinkmann, Kenta Noguchi, Heidi Van den Camp

For each $� � � � � c � � \geq � � 1 � � �$ , we prove tight lower bounds on face sizes that must be present to allow 1- or 2-cuts in simple duals of $� � � � � c � � �$ -connected maps. Using these bounds, we determine the smallest genus on which a $� � � � � c � � �$ -connected map can have a simple dual with a 2-cut and give lower and some upper bounds for the smallest genus on which a $� � � � � c � � �$ -connected map can have a simple dual with a 1-cut.

对于每个c≥1，我们证明了在c连通地图的简单对偶中，必须存在允许1或2切割的面大小的严格下界。利用这些界限，我们确定了c连通映射具有2切简单对偶的最小格，并给出了c连通映射具有a的最小格的下界和上界简单的双刀单切。

{"title":"Face Sizes and the Connectivity of the Dual","authors":"Gunnar Brinkmann, Kenta Noguchi, Heidi Van den Camp","doi":"10.1002/jgt.23277","DOIUrl":"https://doi.org/10.1002/jgt.23277","url":null,"abstract":"For each <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>c</mi>\u0000 \u0000 <mo>≥</mo>\u0000 \u0000 <mn>1</mn>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>, we prove tight lower bounds on face sizes that must be present to allow 1- or 2-cuts in simple duals of <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>c</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>-connected maps. Using these bounds, we determine the smallest genus on which a <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>c</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>-connected map can have a simple dual with a 2-cut and give lower and some upper bounds for the smallest genus on which a <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>c</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>-connected map can have a simple dual with a 1-cut.","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"110 4","pages":"379-391"},"PeriodicalIF":1.0,"publicationDate":"2025-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/jgt.23277","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145272966","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

On Some Algorithmic and Structural Results on Flames 关于火焰的一些算法和结构结果

IF 1 3区数学 Q2 MATHEMATICS

Journal of Graph Theory

Pub Date : 2025-07-13 DOI: 10.1002/jgt.23283

Dávid Szeszlér

A directed graph $� � � � � F � � �$ with a root node $� � � � � r � � �$ is called a flame if for every vertex $� � � � � v � � �$ other than $� � � � � r � � �$ the local edge-connectivity value $� � � � � �_{λ � � F �} � � � (� � � r � �, � � v � � �) � � � �$ from $� � � � � r � � �$ to $� � � � � v � � �$ is equal to $� � � � � �_{ϱ � � F �} � � � (� � v � �) �$

有根节点r的有向图F，如果对每个顶点v都有，则称为火焰图局部边连通性值λ F(r；V)从r到V等于ϱ F (v)v的in度。这是一部经典之作，Lovász[4]的简单而美丽的结果，每个有向图D与根节点r有一个生成子图F是火焰，λ (r)v)的值在F中与在除了r以外的每个顶点v都是D。然而，找到这样一个子图的最小权值的复杂度是开放的[3]。本文证明了该问题在强多项式时间内是可解的。除此之外，我们还证明了火焰通过一个较小的火焰链分解成边缘不相交分支的结果，并以此证明了Lovász的上述定理和Edmonds的经典不相交树杈定理的一个共同推广。

{"title":"On Some Algorithmic and Structural Results on Flames","authors":"Dávid Szeszlér","doi":"10.1002/jgt.23283","DOIUrl":"https://doi.org/10.1002/jgt.23283","url":null,"abstract":"A directed graph <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>F</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> with a root node <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>r</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> is called a flame if for every vertex <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>v</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> other than <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>r</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> the local edge-connectivity value <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <msub>\u0000 <mi>λ</mi>\u0000 \u0000 <mi>F</mi>\u0000 </msub>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mrow>\u0000 <mi>r</mi>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mi>v</mi>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> from <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>r</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> to <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>v</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> is equal to <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <msub>\u0000 <mi>ϱ</mi>\u0000 \u0000 <mi>F</mi>\u0000 </msub>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mi>v</mi>\u0000 \u0000 <mo>)</mo>\u0000 ","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"110 4","pages":"392-397"},"PeriodicalIF":1.0,"publicationDate":"2025-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/jgt.23283","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145272965","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

类型

全部化学•材料生命科学医学物理工程技术环境•农林材料科学地球科学法学管理学化学环境科学与生态学计算机科学教育学经济学农林科学人文科学生物学数学物理与天体物理心理学综合性期刊其他工业工程理学历史学农学文学信息工程

数据库

全部 ACS Publications Elsevier ieeexplore Springer The Royal Society of Chemistry Wiley

期刊

Journal of Graph Theory

全部 Acc. Chem. Res. ACS Applied Bio Materials ACS Appl. Electron. Mater. ACS Appl. Energy Mater. ACS Appl. Mater. Interfaces ACS Appl. Nano Mater. ACS Appl. Polym. Mater. ACS BIOMATER-SCI ENG ACS Catal. ACS Cent. Sci. ACS Chem. Biol. ACS Chemical Health & Safety ACS Chem. Neurosci. ACS Comb. Sci. ACS Earth Space Chem. ACS Energy Lett. ACS Infect. Dis. ACS Macro Lett. ACS Mater. Lett. ACS Med. Chem. Lett. ACS Nano ACS Omega ACS Photonics ACS Sens. ACS Sustainable Chem. Eng. ACS Synth. Biol. Anal. Chem. BIOCHEMISTRY-US Bioconjugate Chem. BIOMACROMOLECULES Chem. Res. Toxicol. Chem. Rev. Chem. Mater. CRYST GROWTH DES ENERG FUEL Environ. Sci. Technol. Environ. Sci. Technol. Lett. Eur. J. Inorg. Chem. IND ENG CHEM RES Inorg. Chem. J. Agric. Food. Chem. J. Chem. Eng. Data J. Chem. Educ. J. Chem. Inf. Model. J. Chem. Theory Comput. J. Med. Chem. J. Nat. Prod. J PROTEOME RES J. Am. Chem. Soc. LANGMUIR MACROMOLECULES Mol. Pharmaceutics Nano Lett. Org. Lett. ORG PROCESS RES DEV ORGANOMETALLICS J. Org. Chem. J. Phys. Chem. J. Phys. Chem. A J. Phys. Chem. B J. Phys. Chem. C J. Phys. Chem. Lett. Analyst Anal. Methods Biomater. Sci. Catal. Sci. Technol. Chem. Commun. Chem. Soc. Rev. CHEM EDUC RES PRACT CRYSTENGCOMM Dalton Trans. Energy Environ. Sci. ENVIRON SCI-NANO ENVIRON SCI-PROC IMP ENVIRON SCI-WAT RES Faraday Discuss. Food Funct. Green Chem. Inorg. Chem. Front. Integr. Biol. J. Anal. At. Spectrom. J. Mater. Chem. A J. Mater. Chem. B J. Mater. Chem. C Lab Chip Mater. Chem. Front. Mater. Horiz. MEDCHEMCOMM Metallomics Mol. Biosyst. Mol. Syst. Des. Eng. Nanoscale Nanoscale Horiz. Nat. Prod. Rep. New J. Chem. Org. Biomol. Chem. Org. Chem. Front. PHOTOCH PHOTOBIO SCI PCCP Polym. Chem.

﹀

微信

客服QQ

扫码关注我们

反馈

Book学术文献互助群
群号：604180095

文献互助智能选刊最新文献互助须知联系我们：info@booksci.cn

Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。