发布求助
文献互助 智能选刊 最新文献

Combinatorica最新文献

筛选
英文 中文
Perfect Matchings in Random Sparsifications of Dirac Hypergraphs 狄拉克超图随机稀疏化中的完美匹配
IF 1.1 2区 数学
Combinatorica Pub Date : 2024-08-05 DOI: 10.1007/s00493-024-00116-0
Dong Yeap Kang, Tom Kelly, Daniela Kühn, Deryk Osthus, Vincent Pfenninger
{"title":"Perfect Matchings in Random Sparsifications of Dirac Hypergraphs","authors":"Dong Yeap Kang, Tom Kelly, Daniela Kühn, Deryk Osthus, Vincent Pfenninger","doi":"10.1007/s00493-024-00116-0","DOIUrl":"https://doi.org/10.1007/s00493-024-00116-0","url":null,"abstract":"<p>For all integers <span>(n ge k &gt; d ge 1)</span>, let <span>(m_{d}(k,n))</span> be the minimum integer <span>(D ge 0)</span> such that every <i>k</i>-uniform <i>n</i>-vertex hypergraph <span>({mathcal {H}})</span> with minimum <i>d</i>-degree <span>(delta _{d}({mathcal {H}}))</span> at least <i>D</i> has an optimal matching. For every fixed integer <span>(k ge 3)</span>, we show that for <span>(n in k mathbb {N})</span> and <span>(p = Omega (n^{-k+1} log n))</span>, if <span>({mathcal {H}})</span> is an <i>n</i>-vertex <i>k</i>-uniform hypergraph with <span>(delta _{k-1}({mathcal {H}}) ge m_{k-1}(k,n))</span>, then a.a.s. its <i>p</i>-random subhypergraph <span>({mathcal {H}}_p)</span> contains a perfect matching. Moreover, for every fixed integer <span>(d &lt; k)</span> and <span>(gamma &gt; 0)</span>, we show that the same conclusion holds if <span>({mathcal {H}})</span> is an <i>n</i>-vertex <i>k</i>-uniform hypergraph with <span>(delta _d({mathcal {H}}) ge m_{d}(k,n) + gamma left( {begin{array}{c}n - d k - dend{array}}right) )</span>. Both of these results strengthen Johansson, Kahn, and Vu’s seminal solution to Shamir’s problem and can be viewed as “robust” versions of hypergraph Dirac-type results. In addition, we also show that in both cases above, <span>({mathcal {H}})</span> has at least <span>(exp ((1-1/k)n log n - Theta (n)))</span> many perfect matchings, which is best possible up to an <span>(exp (Theta (n)))</span> factor.</p>","PeriodicalId":50666,"journal":{"name":"Combinatorica","volume":"3 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141891849","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}
引用次数: 0
A Whitney Type Theorem for Surfaces: Characterising Graphs with Locally Planar Embeddings 曲面的惠特尼型定理：用局部平面嵌入描述图形的特征
IF 1.1 2区 数学
Combinatorica Pub Date : 2024-07-23 DOI: 10.1007/s00493-024-00118-y
Johannes Carmesin
{"title":"A Whitney Type Theorem for Surfaces: Characterising Graphs with Locally Planar Embeddings","authors":"Johannes Carmesin","doi":"10.1007/s00493-024-00118-y","DOIUrl":"https://doi.org/10.1007/s00493-024-00118-y","url":null,"abstract":"<p>Given a graph <i>G</i> and a parameter <i>r</i>, we define the <i>r</i>-<i>local matroid</i> of <i>G</i> to be the matroid generated by its cycles of length at most <i>r</i>. Extending Whitney’s abstract planar duality theorem from 1932, we prove that for every <i>r</i> the <i>r</i>-local matroid of <i>G</i> is co-graphic if and only if <i>G</i> admits a certain type of embedding in a surface, which we call <i>r</i>-<i>planar embedding</i>. The maximum value of <i>r</i> such that a graph <i>G</i> admits an <i>r</i>-planar embedding is closely related to face-width, and such embeddings for this maximum value of <i>r</i> are quite often embeddings of minimum genus. Unlike minimum genus embeddings, these <i>r</i>-planar embeddings can be computed in polynomial time. This provides the first systematic and polynomially computable method to construct for every graph <i>G</i> a surface so that <i>G</i> embeds in that surface in an optimal way (phrased in our notion of <i>r</i>-planarity).</p>","PeriodicalId":50666,"journal":{"name":"Combinatorica","volume":"16 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141755432","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}
引用次数: 0
Storage Codes on Coset Graphs with Asymptotically Unit Rate 具有渐近单位速率的余集图存储代码
IF 1.1 2区 数学
Combinatorica Pub Date : 2024-07-23 DOI: 10.1007/s00493-024-00114-2
Alexander Barg, Moshe Schwartz, Lev Yohananov
{"title":"Storage Codes on Coset Graphs with Asymptotically Unit Rate","authors":"Alexander Barg, Moshe Schwartz, Lev Yohananov","doi":"10.1007/s00493-024-00114-2","DOIUrl":"https://doi.org/10.1007/s00493-024-00114-2","url":null,"abstract":"<p>A storage code on a graph <i>G</i> is a set of assignments of symbols to the vertices such that every vertex can recover its value by looking at its neighbors. We consider the question of constructing large-size storage codes on triangle-free graphs constructed as coset graphs of binary linear codes. Previously it was shown that there are infinite families of binary storage codes on coset graphs with rate converging to 3/4. Here we show that codes on such graphs can attain rate asymptotically approaching 1. Equivalently, this question can be phrased as a version of hat-guessing games on graphs (e.g., Cameron et al., in: Electron J Combin 23(1):48, 2016). In this language, we construct triangle-free graphs with success probability of the players approaching one as the number of vertices tends to infinity. Furthermore, finding linear index codes of rate approaching zero is also an equivalent problem.</p>","PeriodicalId":50666,"journal":{"name":"Combinatorica","volume":"50 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141755351","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}
引用次数: 0
Unavoidable Flats in Matroids Representable over Prime Fields 可在素域上表示的矩阵中不可避免的平面
IF 1.1 2区 数学
Combinatorica Pub Date : 2024-07-11 DOI: 10.1007/s00493-024-00112-4
Jim Geelen, Matthew E. Kroeker
{"title":"Unavoidable Flats in Matroids Representable over Prime Fields","authors":"Jim Geelen, Matthew E. Kroeker","doi":"10.1007/s00493-024-00112-4","DOIUrl":"https://doi.org/10.1007/s00493-024-00112-4","url":null,"abstract":"<p>We show that, for any prime <i>p</i> and integer <span>(k ge 2)</span>, a simple <span>({{,textrm{GF},}}(p))</span>-representable matroid with sufficiently high rank has a rank-<i>k</i> flat which is either independent in <i>M</i>, or is a projective or affine geometry. As a corollary we obtain a Ramsey-type theorem for <span>({{,textrm{GF},}}(p))</span>-representable matroids. For any prime <i>p</i> and integer <span>(kge 2)</span>, if we 2-colour the elements in any simple <span>({{,textrm{GF},}}(p))</span>-representable matroid with sufficiently high rank, then there is a monochromatic flat of rank <i>k</i>.</p>","PeriodicalId":50666,"journal":{"name":"Combinatorica","volume":"89 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141597634","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}
引用次数: 0
On Pisier Type Theorems 论皮西埃类型定理
IF 1.1 2区 数学
Combinatorica Pub Date : 2024-07-11 DOI: 10.1007/s00493-024-00115-1
Jaroslav Nešetřil, Vojtěch Rödl, Marcelo Sales
{"title":"On Pisier Type Theorems","authors":"Jaroslav Nešetřil, Vojtěch Rödl, Marcelo Sales","doi":"10.1007/s00493-024-00115-1","DOIUrl":"https://doi.org/10.1007/s00493-024-00115-1","url":null,"abstract":"<p>For any integer <span>(hgeqslant 2)</span>, a set of integers <span>(B={b_i}_{iin I})</span> is a <span>(B_h)</span>-set if all <i>h</i>-sums <span>(b_{i_1}+ldots +b_{i_h})</span> with <span>(i_1&lt;ldots &lt;i_h)</span> are distinct. Answering a question of Alon and Erdős [2], for every <span>(hgeqslant 2)</span> we construct a set of integers <i>X</i> which is not a union of finitely many <span>(B_h)</span>-sets, yet any finite subset <span>(Ysubseteq X)</span> contains an <span>(B_h)</span>-set <i>Z</i> with <span>(|Z|geqslant varepsilon |Y|)</span>, where <span>(varepsilon :=varepsilon (h))</span>. We also discuss questions related to a problem of Pisier about the existence of a set <i>A</i> with similar properties when replacing <span>(B_h)</span>-sets by the requirement that all finite sums <span>(sum _{jin J}b_j)</span> are distinct.</p>","PeriodicalId":50666,"journal":{"name":"Combinatorica","volume":"18 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141597635","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}
引用次数: 0
Reconstruction in One Dimension from Unlabeled Euclidean Lengths 从无标注的欧氏长度重建一维图像
IF 1.1 2区 数学
Combinatorica Pub Date : 2024-07-11 DOI: 10.1007/s00493-024-00119-x
Robert Connelly, Steven J. Gortler, Louis Theran
{"title":"Reconstruction in One Dimension from Unlabeled Euclidean Lengths","authors":"Robert Connelly, Steven J. Gortler, Louis Theran","doi":"10.1007/s00493-024-00119-x","DOIUrl":"https://doi.org/10.1007/s00493-024-00119-x","url":null,"abstract":"<p>Let <i>G</i> be a 3-connected ordered graph with <i>n</i> vertices and <i>m</i> edges. Let <span>(textbf{p})</span> be a randomly chosen mapping of these <i>n</i> vertices to the integer range <span>({1, 2,3, ldots , 2^b})</span> for <span>(bge m^2)</span>. Let <span>(ell )</span> be the vector of <i>m</i> Euclidean lengths of <i>G</i>’s edges under <span>(textbf{p})</span>. In this paper, we show that, with high probability over <span>(textbf{p})</span>, we can efficiently reconstruct both <i>G</i> and <span>(textbf{p})</span> from <span>(ell )</span>. This reconstruction problem is NP-HARD in the worst case, even if both <i>G</i> and <span>(ell )</span> are given. We also show that our results stand in the presence of small amounts of error in <span>(ell )</span>, and in the real setting, with sufficiently accurate length measurements. Our method combines lattice reduction, which has previously been used to solve random subset sum problems, with an algorithm of Seymour that can efficiently reconstruct an ordered graph given an independence oracle for its matroid.</p>","PeriodicalId":50666,"journal":{"name":"Combinatorica","volume":"39 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141597580","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}
引用次数: 0
On Directed and Undirected Diameters of Vertex-Transitive Graphs 论顶点变换图的有向和无向直径
IF 1.1 2区 数学
Combinatorica Pub Date : 2024-07-09 DOI: 10.1007/s00493-024-00120-4
Saveliy V. Skresanov
{"title":"On Directed and Undirected Diameters of Vertex-Transitive Graphs","authors":"Saveliy V. Skresanov","doi":"10.1007/s00493-024-00120-4","DOIUrl":"https://doi.org/10.1007/s00493-024-00120-4","url":null,"abstract":"<p>A directed diameter of a directed graph is the maximum possible distance between a pair of vertices, where paths must respect edge orientations, while undirected diameter is the diameter of the undirected graph obtained by symmetrizing the edges. In 2006 Babai proved that for a connected directed Cayley graph on <span>( n )</span> vertices the directed diameter is bounded above by a polynomial in undirected diameter and <span>( log n )</span>. Moreover, Babai conjectured that a similar bound holds for vertex-transitive graphs. We prove this conjecture of Babai, in fact, it follows from a more general bound for connected relations of homogeneous coherent configurations. The main novelty of the proof is a generalization of Ruzsa’s triangle inequality from additive combinatorics to the setting of graphs</p>","PeriodicalId":50666,"journal":{"name":"Combinatorica","volume":"2015 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141561508","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}
引用次数: 0
Bounding the Diameter and Eigenvalues of Amply Regular Graphs via Lin–Lu–Yau Curvature 通过林-路-尤曲率限定完全规则图的直径和特征值
IF 1.1 2区 数学
Combinatorica Pub Date : 2024-07-09 DOI: 10.1007/s00493-024-00113-3
Xueping Huang, Shiping Liu, Qing Xia
{"title":"Bounding the Diameter and Eigenvalues of Amply Regular Graphs via Lin–Lu–Yau Curvature","authors":"Xueping Huang, Shiping Liu, Qing Xia","doi":"10.1007/s00493-024-00113-3","DOIUrl":"https://doi.org/10.1007/s00493-024-00113-3","url":null,"abstract":"<p>An amply regular graph is a regular graph such that any two adjacent vertices have <span>(alpha )</span> common neighbors and any two vertices with distance 2 have <span>(beta )</span> common neighbors. We prove a sharp lower bound estimate for the Lin–Lu–Yau curvature of any amply regular graph with girth 3 and <span>(beta &gt;alpha )</span>. The proof involves new ideas relating discrete Ricci curvature with local matching properties: This includes a novel construction of a regular bipartite graph from the local structure and related distance estimates. As a consequence, we obtain sharp diameter and eigenvalue bounds for amply regular graphs.</p>","PeriodicalId":50666,"journal":{"name":"Combinatorica","volume":"51 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141561513","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}
引用次数: 0
Links and the Diaconis–Graham Inequality 链接与迪亚科尼斯-格雷厄姆不平等现象
IF 1.1 2区 数学
Combinatorica Pub Date : 2024-06-27 DOI: 10.1007/s00493-024-00107-1
Christopher Cornwell, Nathan McNew
{"title":"Links and the Diaconis–Graham Inequality","authors":"Christopher Cornwell, Nathan McNew","doi":"10.1007/s00493-024-00107-1","DOIUrl":"https://doi.org/10.1007/s00493-024-00107-1","url":null,"abstract":"<p>In 1977 Diaconis and Graham proved two inequalities relating different measures of disarray in permutations, and asked for a characterization of those permutations for which equality holds in one of these inequalities. Such a characterization was first given in 2013. Recently, another characterization was given by Woo, using a topological link in <span>({mathbb {R}}^3)</span> that can be associated to the cycle diagram of a permutation. We show that Woo’s characterization extends much further: for any permutation, the discrepancy in Diaconis and Graham’s inequality is directly related to the Euler characteristic of the associated link. This connection provides a new proof of the original result of Diaconis and Graham. We also characterize permutations with a fixed discrepancy in terms of their associated links and find that the stabilized-interval-free permutations are precisely those whose associated links are nonsplit.</p>","PeriodicalId":50666,"journal":{"name":"Combinatorica","volume":"23 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141462527","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}
引用次数: 0
Neighborhood Complexity of Planar Graphs 平面图的邻域复杂性
IF 1.1 2区 数学
Combinatorica Pub Date : 2024-06-24 DOI: 10.1007/s00493-024-00110-6
Gwenaël Joret, Clément Rambaud
{"title":"Neighborhood Complexity of Planar Graphs","authors":"Gwenaël Joret, Clément Rambaud","doi":"10.1007/s00493-024-00110-6","DOIUrl":"https://doi.org/10.1007/s00493-024-00110-6","url":null,"abstract":"<p>Reidl et al. (Eur J Comb 75:152–168, 2019) characterized graph classes of bounded expansion as follows: A class <span>({mathcal {C}})</span> closed under subgraphs has bounded expansion if and only if there exists a function <span>(f:{mathbb {N}} rightarrow {mathbb {N}})</span> such that for every graph <span>(G in {mathcal {C}})</span>, every nonempty subset <i>A</i> of vertices in <i>G</i> and every nonnegative integer <i>r</i>, the number of distinct intersections between <i>A</i> and a ball of radius <i>r</i> in <i>G</i> is at most <i>f</i>(<i>r</i>) |<i>A</i>|. When <span>({mathcal {C}})</span> has bounded expansion, the function <i>f</i>(<i>r</i>) coming from existing proofs is typically exponential. In the special case of planar graphs, it was conjectured by Sokołowski (Electron J Comb 30(2):P2.3, 2023) that <i>f</i>(<i>r</i>) could be taken to be a polynomial. In this paper, we prove this conjecture: For every nonempty subset <i>A</i> of vertices in a planar graph <i>G</i> and every nonnegative integer <i>r</i>, the number of distinct intersections between <i>A</i> and a ball of radius <i>r</i> in <i>G</i> is <span>({{,mathrm{{mathcal {O}}},}}(r^4 |A|))</span>. We also show that a polynomial bound holds more generally for every proper minor-closed class of graphs.\u0000</p>","PeriodicalId":50666,"journal":{"name":"Combinatorica","volume":"30 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141444858","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}
引用次数: 0
首页 上一页 下一页 尾页
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整，为了账户安全，请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
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。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号：481959085
Book学术官方微信