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A characterization of weight-regular partitions of graphs 图的权规则分区的表征
Electronic Notes in Discrete Mathematics Pub Date : 2018-07-01 Epub Date: 2018-07-17 DOI: 10.1016/j.endm.2018.06.050
Aida Abiad
{"title":"A characterization of weight-regular partitions of graphs","authors":"Aida Abiad","doi":"10.1016/j.endm.2018.06.050","DOIUrl":"10.1016/j.endm.2018.06.050","url":null,"abstract":"<div><p>A partition <span><math><mi>P</mi><mo>=</mo><mo>{</mo><msub><mrow><mi>V</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>V</mi></mrow><mrow><mi>m</mi></mrow></msub><mo>}</mo></math></span> of the vertex set <em>V</em> of a graph is regular if, for all <em>i</em>, <em>j</em>, the number of neighbors which a vertex in <em>V</em><sub><em>i</em></sub> has in the set <em>V</em><sub><em>j</em></sub> is independent of the choice of vertex in <em>V</em><sub><em>i</em></sub>. The natural generalization of a regular partition, which makes sense also for non-regular graphs, is the so-called weight-regular partition, which gives to each vertex <span><math><mi>u</mi><mo>∈</mo><mi>V</mi></math></span> a weight which equals the corresponding entry <span><math><msub><mrow><mi>ν</mi></mrow><mrow><mi>u</mi></mrow></msub></math></span> of the Perron eigenvector <strong><em>ν</em></strong>. In this work we investigate when a weight-regular partition of a graph is regular in terms of double stochastic matrices. Inspired by a characterization of regular graphs by Hoffman, we provide a new characterization of weight-regular partitions by using a Hoffman-like polynomial.</p></div>","PeriodicalId":35408,"journal":{"name":"Electronic Notes in Discrete Mathematics","volume":"68 ","pages":"Pages 293-298"},"PeriodicalIF":0.0,"publicationDate":"2018-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.endm.2018.06.050","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122608715","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
Graphs preserving total distance upon vertex removal 顶点移除后保持总距离的图
Electronic Notes in Discrete Mathematics Pub Date : 2018-07-01 Epub Date: 2018-07-17 DOI: 10.1016/j.endm.2018.06.019
Snježana Majstorović, Martin Knor, Riste Škrekovski
{"title":"Graphs preserving total distance upon vertex removal","authors":"Snježana Majstorović,&nbsp;Martin Knor,&nbsp;Riste Škrekovski","doi":"10.1016/j.endm.2018.06.019","DOIUrl":"10.1016/j.endm.2018.06.019","url":null,"abstract":"<div><p>The total distance or Wiener index <span><math><mi>W</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span> of a connected graph <em>G</em> is defined as the sum of distances between all pairs of vertices in <em>G</em>. In 1991, Šoltés posed the problem of finding all graphs <em>G</em> such that the equality <span><math><mi>W</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>=</mo><mi>W</mi><mo>(</mo><mi>G</mi><mo>−</mo><mi>v</mi><mo>)</mo></math></span> holds for all their vertices <em>v</em>. Up to now, the only known graph with this property is the cycle <em>C</em><sub>11</sub>. Our main object of study is a relaxed version of this problem: Find graphs for which total distance does not change when a particular vertex is removed. We show that there are infinitely many graphs that satisfy this property. This gives hope that Šoltes's problem may have also some solutions distinct from <em>C</em><sub>11</sub>.</p></div>","PeriodicalId":35408,"journal":{"name":"Electronic Notes in Discrete Mathematics","volume":"68 ","pages":"Pages 107-112"},"PeriodicalIF":0.0,"publicationDate":"2018-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.endm.2018.06.019","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123866768","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: 1
Dyck-Eulerian digraphs Dyck-Eulerian标识
Electronic Notes in Discrete Mathematics Pub Date : 2018-07-01 Epub Date: 2018-07-17 DOI: 10.1016/j.endm.2018.06.041
Pietro Codara , Ottavio M. D'Antona
{"title":"Dyck-Eulerian digraphs","authors":"Pietro Codara ,&nbsp;Ottavio M. D'Antona","doi":"10.1016/j.endm.2018.06.041","DOIUrl":"10.1016/j.endm.2018.06.041","url":null,"abstract":"<div><p>We introduce a family of Eulerian digraphs, <span><math><mi>E</mi></math></span>, associated with Dyck words. We provide the algorithms implementing the bijection between <span><math><mi>E</mi></math></span> and <span><math><mi>W</mi></math></span>, the set of Dyck words. To do so, we exploit a binary matrix, that we call <em>Dyck matrix</em>, representing the cycles of an Eulerian digraph.</p></div>","PeriodicalId":35408,"journal":{"name":"Electronic Notes in Discrete Mathematics","volume":"68 ","pages":"Pages 239-244"},"PeriodicalIF":0.0,"publicationDate":"2018-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.endm.2018.06.041","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124985359","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
Some clustering algorithms in normed planes 规范平面上的一些聚类算法
Electronic Notes in Discrete Mathematics Pub Date : 2018-07-01 Epub Date: 2018-07-17 DOI: 10.1016/j.endm.2018.06.033
Pedro Martín , Diego Yáñez
{"title":"Some clustering algorithms in normed planes","authors":"Pedro Martín ,&nbsp;Diego Yáñez","doi":"10.1016/j.endm.2018.06.033","DOIUrl":"10.1016/j.endm.2018.06.033","url":null,"abstract":"<div><p>Given two sets of points <em>A</em> and <em>B</em> in a normed plane, we prove that there are two linearly separable sets <span><math><msup><mrow><mi>A</mi></mrow><mrow><mo>′</mo></mrow></msup></math></span> and <span><math><msup><mrow><mi>B</mi></mrow><mrow><mo>′</mo></mrow></msup></math></span> such that <span><math><mrow><mi>diam</mi></mrow><mo>(</mo><msup><mrow><mi>A</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>)</mo><mo>≤</mo><mrow><mi>diam</mi></mrow><mo>(</mo><mi>A</mi><mo>)</mo><mo>,</mo><mrow><mi>diam</mi></mrow><mo>(</mo><msup><mrow><mi>B</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>)</mo><mo>≤</mo><mrow><mi>diam</mi></mrow><mo>(</mo><mi>B</mi><mo>)</mo></math></span>, and <span><math><msup><mrow><mi>A</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>∪</mo><msup><mrow><mi>B</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>=</mo><mi>A</mi><mo>∪</mo><mi>B</mi></math></span>. As a result, some Euclidean clustering algorithms are adapted to normed planes, for instance, those that minimize the maximum, the sum, or the sum of squares of the diameters (or the radii) of <em>k</em> clusters. Some specific solutions are presented for <span><math><mi>k</mi><mo>=</mo><mn>2</mn></math></span> and <span><math><mi>k</mi><mo>=</mo><mn>3</mn></math></span> that minimize the diameter of the clusters. The 2-clustering problem when two different bounds are imposed to the diameters is also studied.</p></div>","PeriodicalId":35408,"journal":{"name":"Electronic Notes in Discrete Mathematics","volume":"68 ","pages":"Pages 191-196"},"PeriodicalIF":0.0,"publicationDate":"2018-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.endm.2018.06.033","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129740422","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
On the discrete Brunn-Minkowski inequality by Gradner&Gronchi 关于离散Brunn-Minkowski不等式的Gradner&Gronchi
Electronic Notes in Discrete Mathematics Pub Date : 2018-07-01 Epub Date: 2018-07-17 DOI: 10.1016/j.endm.2018.06.051
David Iglesias
{"title":"On the discrete Brunn-Minkowski inequality by Gradner&Gronchi","authors":"David Iglesias","doi":"10.1016/j.endm.2018.06.051","DOIUrl":"10.1016/j.endm.2018.06.051","url":null,"abstract":"<div><p>In 2002 Gardner and Gronchi obtained a discrete analogue of the Brunn-Minkowski inequality. They proved that for finite subsets <span><math><mi>A</mi><mo>,</mo><mi>B</mi><mo>⊂</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> with <span><math><mi>dim</mi><mo>⁡</mo><mi>B</mi><mo>=</mo><mi>n</mi></math></span>, the inequality <span><math><mo>|</mo><mi>A</mi><mo>+</mo><mi>B</mi><mo>|</mo><mo>≥</mo><mo>|</mo><msubsup><mrow><mi>D</mi></mrow><mrow><mo>|</mo><mi>A</mi><mo>|</mo></mrow><mrow><mi>B</mi></mrow></msubsup><mo>+</mo><msubsup><mrow><mi>D</mi></mrow><mrow><mo>|</mo><mi>B</mi><mo>|</mo></mrow><mrow><mi>B</mi></mrow></msubsup><mo>|</mo></math></span> holds, where <span><math><msubsup><mrow><mi>D</mi></mrow><mrow><mo>|</mo><mi>A</mi><mo>|</mo></mrow><mrow><mi>B</mi></mrow></msubsup><mo>,</mo><msubsup><mrow><mi>D</mi></mrow><mrow><mo>|</mo><mi>B</mi><mo>|</mo></mrow><mrow><mi>B</mi></mrow></msubsup></math></span> are particular subsets of the integer lattice, called <em>B</em>-initial segments. The aim of this paper is to provide a method in order to compute <span><math><mo>|</mo><msubsup><mrow><mi>D</mi></mrow><mrow><mo>|</mo><mi>A</mi><mo>|</mo></mrow><mrow><mi>B</mi></mrow></msubsup><mo>+</mo><msubsup><mrow><mi>D</mi></mrow><mrow><mo>|</mo><mi>B</mi><mo>|</mo></mrow><mrow><mi>B</mi></mrow></msubsup><mo>|</mo></math></span> and so, to implement this inequality.</p></div>","PeriodicalId":35408,"journal":{"name":"Electronic Notes in Discrete Mathematics","volume":"68 ","pages":"Pages 299-304"},"PeriodicalIF":0.0,"publicationDate":"2018-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.endm.2018.06.051","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132003594","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
On characterizing the extreme points of the generalized transitive tournament polytope 关于广义可传递竞赛多面体极值点的刻画
Electronic Notes in Discrete Mathematics Pub Date : 2018-07-01 Epub Date: 2018-07-17 DOI: 10.1016/j.endm.2018.06.047
Konstantinos Papalamprou
{"title":"On characterizing the extreme points of the generalized transitive tournament polytope","authors":"Konstantinos Papalamprou","doi":"10.1016/j.endm.2018.06.047","DOIUrl":"10.1016/j.endm.2018.06.047","url":null,"abstract":"<div><p>A non-negative <span><math><mi>n</mi><mo>×</mo><mi>n</mi></math></span> matrix [<span><math><msub><mrow><mi>x</mi></mrow><mrow><mi>i</mi><mi>j</mi></mrow></msub></math></span>] is called generalized tournament, denoted GTT(n), if: <span><math><msub><mrow><mi>x</mi></mrow><mrow><mi>i</mi><mi>i</mi></mrow></msub><mo>=</mo><mn>0</mn></math></span> (for all i), <span><math><msub><mrow><mi>x</mi></mrow><mrow><mi>i</mi><mi>j</mi></mrow></msub><mo>+</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>j</mi><mi>i</mi></mrow></msub><mo>=</mo><mn>1</mn></math></span> (for all(i,j) with <span><math><mi>i</mi><mo>≠</mo><mi>j</mi></math></span>) and <span><math><mn>1</mn><mo>≤</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>i</mi><mi>j</mi></mrow></msub><mo>+</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>j</mi><mi>k</mi></mrow></msub><mo>+</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>k</mi><mi>i</mi></mrow></msub><mo>≤</mo><mn>2</mn></math></span> (for all (i,j,k) with <span><math><mi>i</mi><mo>,</mo><mi>j</mi><mo>,</mo><mi>k</mi></math></span> pairwise distinct). In [9], using hypergraphs associated with GTT matrices, it has been shown that for <span><math><mi>n</mi><mo>≤</mo><mn>6</mn></math></span> all the vertices of the GTT(n) polytope are half-integral. In this work, we show that these matrices belong to the class of 2-regular matrices and highlight the related optimization implications. Finally, based on our approach and known partial results, conjectures on characterizing the extreme points of the GTT(n) polytope for <span><math><mi>n</mi><mo>≥</mo><mn>7</mn></math></span> are provided.</p></div>","PeriodicalId":35408,"journal":{"name":"Electronic Notes in Discrete Mathematics","volume":"68 ","pages":"Pages 275-280"},"PeriodicalIF":0.0,"publicationDate":"2018-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.endm.2018.06.047","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121136628","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
Set systems with distinct sumsets 集合具有不同集合的系统
Electronic Notes in Discrete Mathematics Pub Date : 2018-07-01 Epub Date: 2018-07-17 DOI: 10.1016/j.endm.2018.06.004
Javier Cilleruelo , Oriol Serra , Maximilian Wötzel
{"title":"Set systems with distinct sumsets","authors":"Javier Cilleruelo ,&nbsp;Oriol Serra ,&nbsp;Maximilian Wötzel","doi":"10.1016/j.endm.2018.06.004","DOIUrl":"10.1016/j.endm.2018.06.004","url":null,"abstract":"<div><p>A family <span><math><mi>A</mi></math></span> of <em>k</em>-subsets of <span><math><mo>{</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mo>…</mo><mo>,</mo><mi>N</mi><mo>}</mo></math></span> is a Sidon system if the sumsets <span><math><mi>A</mi><mo>+</mo><msup><mrow><mi>A</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>,</mo><mi>A</mi><mo>,</mo><msup><mrow><mi>A</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>∈</mo><mi>A</mi></math></span> are pairwise distinct. We show that the largest cardinality <span><math><msub><mrow><mi>F</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>(</mo><mi>N</mi><mo>)</mo></math></span> of a Sidon system of <em>k</em>-subsets of <span><math><mo>[</mo><mi>N</mi><mo>]</mo></math></span> satisfies <span><math><msub><mrow><mi>F</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>(</mo><mi>N</mi><mo>)</mo><mo>≤</mo><mrow><mo>(</mo><mtable><mtr><mtd><mrow><mi>N</mi><mo>−</mo><mn>1</mn></mrow></mtd></mtr><mtr><mtd><mrow><mi>k</mi><mo>−</mo><mn>1</mn></mrow></mtd></mtr></mtable><mo>)</mo></mrow><mo>+</mo><mi>N</mi><mo>−</mo><mi>k</mi></math></span> and the asymptotic lower bound <span><math><msub><mrow><mi>F</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>(</mo><mi>N</mi><mo>)</mo><mo>=</mo><msub><mrow><mi>Ω</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>(</mo><msup><mrow><mi>N</mi></mrow><mrow><mi>k</mi><mo>−</mo><mn>1</mn></mrow></msup><mo>)</mo></math></span>. More precise bounds on <span><math><msub><mrow><mi>F</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>(</mo><mi>N</mi><mo>)</mo></math></span> are obtained for <span><math><mi>k</mi><mo>≤</mo><mn>3</mn></math></span>. We also obtain the threshold probability for a random system to be Sidon for <span><math><mi>k</mi><mo>=</mo><mn>2</mn></math></span> and 3.</p></div>","PeriodicalId":35408,"journal":{"name":"Electronic Notes in Discrete Mathematics","volume":"68 ","pages":"Pages 17-22"},"PeriodicalIF":0.0,"publicationDate":"2018-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.endm.2018.06.004","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127014072","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
Two-line graphs of partial Latin rectangles 部分拉丁矩形的双线图
Electronic Notes in Discrete Mathematics Pub Date : 2018-07-01 Epub Date: 2018-07-17 DOI: 10.1016/j.endm.2018.06.010
Eiran Danan, Raúl M. Falcón, Dani Kotlar, Trent G. Marbach, Rebecca J. Stones
{"title":"Two-line graphs of partial Latin rectangles","authors":"Eiran Danan,&nbsp;Raúl M. Falcón,&nbsp;Dani Kotlar,&nbsp;Trent G. Marbach,&nbsp;Rebecca J. Stones","doi":"10.1016/j.endm.2018.06.010","DOIUrl":"10.1016/j.endm.2018.06.010","url":null,"abstract":"<div><p>Two-line graphs of a given partial Latin rectangle are introduced as vertex-and-edge-coloured bipartite graphs that give rise to new autotopism invariants. They reduce the complexity of any currently known method for computing autotopism groups of partial Latin rectangles.</p></div>","PeriodicalId":35408,"journal":{"name":"Electronic Notes in Discrete Mathematics","volume":"68 ","pages":"Pages 53-58"},"PeriodicalIF":0.0,"publicationDate":"2018-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.endm.2018.06.010","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133145514","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
Autoparatopism stabilized colouring games on rook's graphs 自斜视在rook的图形上稳定了着色游戏
Electronic Notes in Discrete Mathematics Pub Date : 2018-07-01 Epub Date: 2018-07-17 DOI: 10.1016/j.endm.2018.06.040
Stephan Dominique Andres, Helena Bergold, Raúl M. Falcón
{"title":"Autoparatopism stabilized colouring games on rook's graphs","authors":"Stephan Dominique Andres,&nbsp;Helena Bergold,&nbsp;Raúl M. Falcón","doi":"10.1016/j.endm.2018.06.040","DOIUrl":"10.1016/j.endm.2018.06.040","url":null,"abstract":"<div><p>We introduce the autoparatopism variant of the autotopism stabilized colouring game on the <span><math><mi>n</mi><mo>×</mo><mi>n</mi></math></span> rook's graph as a natural generalization of the latter so that each board configuration is uniquely related to a partial Latin square of order <em>n</em> that respects a given autoparatopism (<em>θ</em>; <em>π</em>). To this end, we distinguish between <span><math><mi>π</mi><mo>∈</mo><mo>{</mo><mrow><mi>Id</mi></mrow><mo>,</mo><mo>(</mo><mn>12</mn><mo>)</mo><mo>}</mo></math></span> and <span><math><mi>π</mi><mo>∈</mo><mo>{</mo><mo>(</mo><mn>13</mn><mo>)</mo><mo>,</mo><mo>(</mo><mn>23</mn><mo>)</mo><mo>,</mo><mo>(</mo><mn>123</mn><mo>)</mo><mo>,</mo><mo>(</mo><mn>132</mn><mo>)</mo><mo>}</mo></math></span>. The complexity of this variant is examined by means of the autoparatopism stabilized game chromatic number. Some illustrative examples and results are shown.</p></div>","PeriodicalId":35408,"journal":{"name":"Electronic Notes in Discrete Mathematics","volume":"68 ","pages":"Pages 233-238"},"PeriodicalIF":0.0,"publicationDate":"2018-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.endm.2018.06.040","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133425286","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
The Fortress Problem in Terms of the Number of Reflex and Convex Vertices. A 3D objects scanning application 基于反射顶点和凸顶点数量的堡垒问题。一个3D对象扫描应用程序
Electronic Notes in Discrete Mathematics Pub Date : 2018-07-01 Epub Date: 2018-07-17 DOI: 10.1016/j.endm.2018.06.030
Elena Cabrera Revuelta, María José Chávez de Diego , Alberto Márquez Pérez
{"title":"The Fortress Problem in Terms of the Number of Reflex and Convex Vertices. A 3D objects scanning application","authors":"Elena Cabrera Revuelta,&nbsp;María José Chávez de Diego ,&nbsp;Alberto Márquez Pérez","doi":"10.1016/j.endm.2018.06.030","DOIUrl":"10.1016/j.endm.2018.06.030","url":null,"abstract":"<div><p>This work focuses on the visibility of exterior of a polygon. We show a lower bound for the Fortress Problem applied to polygons <em>P</em> having <em>n</em> vertices in terms of the number of reflex vertices, the number of convex vertices and the number of pockets that are found when the convex hull is made on <em>P</em>. The results are related to the task of the geometric data acquisition for architectural surveys through techniques such as laser scanner.</p></div>","PeriodicalId":35408,"journal":{"name":"Electronic Notes in Discrete Mathematics","volume":"68 ","pages":"Pages 173-178"},"PeriodicalIF":0.0,"publicationDate":"2018-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.endm.2018.06.030","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129103490","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: 1
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