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Electronic Notes in Discrete Mathematics最新文献

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Cyclic Automorphism Groups of Graphs and Edge-Colored Graphs 图与边色图的循环自同构群
Electronic Notes in Discrete Mathematics Pub Date : 2018-07-01 DOI: 10.1016/j.endm.2018.06.008
Mariusz Grech, Andrzej Kisielewicz
{"title":"Cyclic Automorphism Groups of Graphs and Edge-Colored Graphs","authors":"Mariusz Grech,&nbsp;Andrzej Kisielewicz","doi":"10.1016/j.endm.2018.06.008","DOIUrl":"10.1016/j.endm.2018.06.008","url":null,"abstract":"<div><p>In this paper we describe the automorphism groups of graphs and edge-colored graphs that are cyclic as permutation groups. In addition, we show that every such group is the automorphism group of a complete graph whose edges are colored with 3 colors, and we characterize those groups that are automorphism groups of simple graphs.</p></div>","PeriodicalId":35408,"journal":{"name":"Electronic Notes in Discrete Mathematics","volume":"68 ","pages":"Pages 41-46"},"PeriodicalIF":0.0,"publicationDate":"2018-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.endm.2018.06.008","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115520990","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
A discretization result for some optimization problems in framework spaces with polyhedral obstacles and the Manhattan metric 具有多面体障碍物的框架空间中若干优化问题的离散化结果
Electronic Notes in Discrete Mathematics Pub Date : 2018-07-01 DOI: 10.1016/j.endm.2018.06.028
Justo Puerto , Moisés Rodríguez-Madrena
{"title":"A discretization result for some optimization problems in framework spaces with polyhedral obstacles and the Manhattan metric","authors":"Justo Puerto ,&nbsp;Moisés Rodríguez-Madrena","doi":"10.1016/j.endm.2018.06.028","DOIUrl":"10.1016/j.endm.2018.06.028","url":null,"abstract":"<div><p>In this work we consider the shortest path problem and the single facility Weber location problem in any real space of finite dimension where there exist different types of polyhedral obstacles or forbidden regions. These regions are polyhedral sets and the metric considered in the space is the Manhattan metric. We present a result that reduce these continuous problems into problems in a “add hoc” graph, where the original problems can be solved using elementary techniques of Graph Theory. We show that, fixed the dimension of the space, both the reduction and the resolution can be done in polynomial time.</p></div>","PeriodicalId":35408,"journal":{"name":"Electronic Notes in Discrete Mathematics","volume":"68 ","pages":"Pages 161-165"},"PeriodicalIF":0.0,"publicationDate":"2018-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.endm.2018.06.028","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123663154","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Hyperplane arrangements between Shi and Ish Shi和Ish之间的超平面排列
Electronic Notes in Discrete Mathematics Pub Date : 2018-07-01 DOI: 10.1016/j.endm.2018.06.046
Rui Duarte , António Guedes de Oliveira
{"title":"Hyperplane arrangements between Shi and Ish","authors":"Rui Duarte ,&nbsp;António Guedes de Oliveira","doi":"10.1016/j.endm.2018.06.046","DOIUrl":"10.1016/j.endm.2018.06.046","url":null,"abstract":"<div><p>We introduce a new family of hyperplane arrangements in dimension <span><math><mi>n</mi><mo>≥</mo><mn>3</mn></math></span> that includes both the Shi arrangement and the Ish arrangement. We prove that all the members of this family have the same number of regions — the connected components of the complement of the union of the hyperplanes — which can be bijectively labeled with the Pak-Stanley labelling. In addition, we characterise the Pak-Stanley labels of the regions of this family of hyperplane arrangements.</p></div>","PeriodicalId":35408,"journal":{"name":"Electronic Notes in Discrete Mathematics","volume":"68 ","pages":"Pages 269-274"},"PeriodicalIF":0.0,"publicationDate":"2018-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.endm.2018.06.046","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125025673","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
New results on production matrices for geometric graphs 几何图的生成矩阵的新结果
Electronic Notes in Discrete Mathematics Pub Date : 2018-07-01 DOI: 10.1016/j.endm.2018.06.037
Guillermo Esteban, Clemens Huemer, Rodrigo I. Silveira
{"title":"New results on production matrices for geometric graphs","authors":"Guillermo Esteban,&nbsp;Clemens Huemer,&nbsp;Rodrigo I. Silveira","doi":"10.1016/j.endm.2018.06.037","DOIUrl":"10.1016/j.endm.2018.06.037","url":null,"abstract":"<div><p>We present novel production matrices for non-crossing partitions, connected geometric graphs, and <em>k</em>-angulations, which provide another way of counting the number of such objects. For instance, a formula for the number of connected geometric graphs with given root degree, drawn on a set of <em>n</em> points in convex position in the plane, is presented. Further, we find the characteristic polynomials and we provide a characterization of the eigenvectors of the production matrices.</p></div>","PeriodicalId":35408,"journal":{"name":"Electronic Notes in Discrete Mathematics","volume":"68 ","pages":"Pages 215-220"},"PeriodicalIF":0.0,"publicationDate":"2018-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.endm.2018.06.037","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126322770","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Geometric quadrangulations of a polygon 多边形的几何四边形
Electronic Notes in Discrete Mathematics Pub Date : 2018-07-01 DOI: 10.1016/j.endm.2018.06.011
Atsuhiro Nakamoto , Gen Kawatani, Naoki Matsumoto, Jorge Urrutia
{"title":"Geometric quadrangulations of a polygon","authors":"Atsuhiro Nakamoto ,&nbsp;Gen Kawatani,&nbsp;Naoki Matsumoto,&nbsp;Jorge Urrutia","doi":"10.1016/j.endm.2018.06.011","DOIUrl":"10.1016/j.endm.2018.06.011","url":null,"abstract":"<div><p>We deal with a <em>geometric quadrangulation</em> of a polygon <em>P</em>. We define a new notion called “the spirality” of <em>P</em>, which measures how close <em>P</em> is from being a convex polygon. Using the spirality, we describe (1) a condition of <em>P</em> to admit a geometric quadrangulation, and (2) a condition of <em>P</em> guaranteeing that any two geometric quadrangulations on <em>P</em> can be related by a sequence of edge flips.</p></div>","PeriodicalId":35408,"journal":{"name":"Electronic Notes in Discrete Mathematics","volume":"68 ","pages":"Pages 59-64"},"PeriodicalIF":0.0,"publicationDate":"2018-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.endm.2018.06.011","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131704617","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
Integral Free-Form Sudoku graphs 积分自由形式数独图
Electronic Notes in Discrete Mathematics Pub Date : 2018-07-01 DOI: 10.1016/j.endm.2018.06.009
Omar Alomari, Mohammad Abudayah, Torsten Sander
{"title":"Integral Free-Form Sudoku graphs","authors":"Omar Alomari,&nbsp;Mohammad Abudayah,&nbsp;Torsten Sander","doi":"10.1016/j.endm.2018.06.009","DOIUrl":"10.1016/j.endm.2018.06.009","url":null,"abstract":"<div><p>A free-form Sudoku puzzle is a square arrangement of <span><math><mi>m</mi><mo>×</mo><mi>m</mi></math></span> cells such that the cells are partitioned into <em>m</em> subsets (called blocks) of equal cardinality. The goal of the puzzle is to place integers <span><math><mn>1</mn><mo>,</mo><mo>…</mo><mi>m</mi></math></span> in the cells such that the numbers in every row, column and block are distinct. Represent each cell by a vertex and add edges between two vertices exactly when the corresponding cells, according to the rules, must contain different numbers. This yields the associated free-form Sudoku graph. It was shown that all Sudoku graphs are integral graphs, in this paper we present many free-form Sudoku graphs that are still integral graphs.</p></div>","PeriodicalId":35408,"journal":{"name":"Electronic Notes in Discrete Mathematics","volume":"68 ","pages":"Pages 47-52"},"PeriodicalIF":0.0,"publicationDate":"2018-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.endm.2018.06.009","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131487574","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The first order convergence law fails for random perfect graphs 对于随机完美图，一阶收敛律失效
Electronic Notes in Discrete Mathematics Pub Date : 2018-07-01 DOI: 10.1016/j.endm.2018.06.013
Tobias Müller, Marc Noy
{"title":"The first order convergence law fails for random perfect graphs","authors":"Tobias Müller,&nbsp;Marc Noy","doi":"10.1016/j.endm.2018.06.013","DOIUrl":"https://doi.org/10.1016/j.endm.2018.06.013","url":null,"abstract":"<div><p>We consider first order expressible properties of random perfect graphs. That is, we pick a graph <span><math><msub><mrow><mi>G</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> uniformly at random from all (labelled) perfect graphs on n vertices and consider the probability that it satisfies some graph property that can be expressed in the first order language of graphs. We show that there exists such a first order expressible property for which the probability that <span><math><msub><mrow><mi>G</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> satisfies it does not converge as <span><math><mi>n</mi><mo>→</mo><mo>∞</mo></math></span>.</p></div>","PeriodicalId":35408,"journal":{"name":"Electronic Notes in Discrete Mathematics","volume":"68 ","pages":"Pages 71-76"},"PeriodicalIF":0.0,"publicationDate":"2018-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.endm.2018.06.013","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138399669","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Finding multiplies solutions for non-linear integer programming 非线性整数规划的乘法求解
Electronic Notes in Discrete Mathematics Pub Date : 2018-07-01 DOI: 10.1016/j.endm.2018.06.022
José Manuel Jiménez Cobano, José María Ucha Enríquez
{"title":"Finding multiplies solutions for non-linear integer programming","authors":"José Manuel Jiménez Cobano,&nbsp;José María Ucha Enríquez","doi":"10.1016/j.endm.2018.06.022","DOIUrl":"10.1016/j.endm.2018.06.022","url":null,"abstract":"<div><p>We explain how to compute all the solutions of a nonlinear integer problem using the algebraic test-sets associated to some linear subproblem. These test-sets are obtained using Gröbner bases. We compare our method with previous approaches.</p></div>","PeriodicalId":35408,"journal":{"name":"Electronic Notes in Discrete Mathematics","volume":"68 ","pages":"Pages 125-130"},"PeriodicalIF":0.0,"publicationDate":"2018-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.endm.2018.06.022","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77725548","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Satisfaction and Power in Unanimous Majority Influence Decision Models 一致多数中的满意度和权力影响决策模型
Electronic Notes in Discrete Mathematics Pub Date : 2018-07-01 DOI: 10.1016/j.endm.2018.06.034
Xavier Molinero , Fabián Riquelme, Maria Serna
{"title":"Satisfaction and Power in Unanimous Majority Influence Decision Models","authors":"Xavier Molinero ,&nbsp;Fabián Riquelme,&nbsp;Maria Serna","doi":"10.1016/j.endm.2018.06.034","DOIUrl":"10.1016/j.endm.2018.06.034","url":null,"abstract":"<div><p>We consider decision models associated with cooperative influence games, the <em>oblivious</em> and the <em>non-oblivious</em> influence models. In those models the <em>satisfaction</em> and the <em>power</em> measures were introduced and studied. We analyze the computational complexity of those measures when the influence level is set to unanimity and the rule of decision is simple majority. We show that computing the satisfaction and the power measure in those systems are #P-hard.</p></div>","PeriodicalId":35408,"journal":{"name":"Electronic Notes in Discrete Mathematics","volume":"68 ","pages":"Pages 197-202"},"PeriodicalIF":0.0,"publicationDate":"2018-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.endm.2018.06.034","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114370676","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 6
Frozen colourings of bounded degree graphs 有界度图的冻结着色
Electronic Notes in Discrete Mathematics Pub Date : 2018-07-01 DOI: 10.1016/j.endm.2018.06.029
Marthe Bonamy, Nicolas Bousquet, Guillem Perarnau
{"title":"Frozen colourings of bounded degree graphs","authors":"Marthe Bonamy,&nbsp;Nicolas Bousquet,&nbsp;Guillem Perarnau","doi":"10.1016/j.endm.2018.06.029","DOIUrl":"10.1016/j.endm.2018.06.029","url":null,"abstract":"<div><p>Let <em>G</em> be a graph with maximum degree Δ and <em>k</em> be an integer. The <em>k</em>-recolouring graph of <em>G</em> is the graph whose vertices are proper <em>k</em>-colourings of <em>G</em> and where two colourings are adjacent iff they differ on exactly one vertex. Feghali, Johnson and Paulusma showed that the (<span><math><mi>Δ</mi><mo>+</mo><mn>1</mn></math></span>)-recolouring graph is composed by a unique connected component and (possibly many) isolated vertices, also known as frozen colourings of <em>G</em>.</p><p>Motivated by its applications to sampling, we study the proportion of frozen colourings of connected graphs. Our main result is that the probability a proper colouring is frozen is exponentially small on the order of the graph. The obtained bound is tight up to a logarithmic factor on Δ in the exponent. We briefly discuss the implications of our result on the study of the Glauber dynamics on (<span><math><mi>Δ</mi><mo>+</mo><mn>1</mn></math></span>)-colourings. Additionally, we show that frozen colourings may exist even for graphs with arbitrary large girth. Finally, we show that typical Δ-regular graphs have no frozen colourings.</p></div>","PeriodicalId":35408,"journal":{"name":"Electronic Notes in Discrete Mathematics","volume":"68 ","pages":"Pages 167-172"},"PeriodicalIF":0.0,"publicationDate":"2018-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.endm.2018.06.029","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125979238","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
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