European Journal of Combinatorics最新文献_第6页

IF 0.9 3区数学

European Journal of Combinatorics Pub Date : 2026-02-01 Epub Date: 2025-11-25 DOI: 10.1016/j.ejc.2025.104285

Nantel Bergeron , Vincent Pilaud

{"title":"Interval hypergraphic lattices","authors":"Nantel Bergeron , Vincent Pilaud","doi":"10.1016/j.ejc.2025.104285","DOIUrl":"10.1016/j.ejc.2025.104285","url":null,"abstract":"<div><div>For a hypergraph <span><math><mi>H</mi></math></span> on <span><math><mrow><mo>[</mo><mi>n</mi><mo>]</mo></mrow></math></span>, the hypergraphic poset <span><math><msub><mrow><mi>P</mi></mrow><mrow><mi>H</mi></mrow></msub></math></span> is the transitive closure of the oriented skeleton of the hypergraphic polytope <span><math><msub><mrow><mo>△</mo></mrow><mrow><mi>H</mi></mrow></msub></math></span> (the Minkowski sum of the standard simplices <span><math><msub><mrow><mo>△</mo></mrow><mrow><mi>H</mi></mrow></msub></math></span> for all <span><math><mrow><mi>H</mi><mo>∈</mo><mi>H</mi></mrow></math></span>). Hypergraphic posets include the weak order for the permutahedron (when <span><math><mi>H</mi></math></span> is the complete graph on <span><math><mrow><mo>[</mo><mi>n</mi><mo>]</mo></mrow></math></span>) and the Tamari lattice for the associahedron (when <span><math><mi>H</mi></math></span> is the set of all intervals of <span><math><mrow><mo>[</mo><mi>n</mi><mo>]</mo></mrow></math></span>), which motivates the study of lattice properties of hypergraphic posets. In this paper, we focus on interval hypergraphs, where all hyperedges are intervals of <span><math><mrow><mo>[</mo><mi>n</mi><mo>]</mo></mrow></math></span>. We characterize the interval hypergraphs <span><math><mi>I</mi></math></span> for which <span><math><msub><mrow><mi>P</mi></mrow><mrow><mi>I</mi></mrow></msub></math></span> is a lattice, a distributive lattice, a semidistributive lattice, and a lattice quotient of the weak order.</div></div>","PeriodicalId":50490,"journal":{"name":"European Journal of Combinatorics","volume":"132 ","pages":"Article 104285"},"PeriodicalIF":0.9,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145623505","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

Morphism extension classes of countable L-colored graphs 可数l色图的态射扩展类

IF 0.9 3区数学

European Journal of Combinatorics Pub Date : 2026-02-01 Epub Date: 2025-10-18 DOI: 10.1016/j.ejc.2025.104256

Andrés Aranda , David Hartman

引用次数: 0

A perfect expansion property 一个完美的展开性质

IF 0.9 3区数学

European Journal of Combinatorics Pub Date : 2026-02-01 Epub Date: 2025-10-15 DOI: 10.1016/j.ejc.2025.104265

Micheal Pawliuk

{"title":"A perfect expansion property","authors":"Micheal Pawliuk","doi":"10.1016/j.ejc.2025.104265","DOIUrl":"10.1016/j.ejc.2025.104265","url":null,"abstract":"<div><div>We present two exact versions of the quantitative expansion property first presented in Angel et al. (2014), called the Perfect Expansion Property and the disjoint Perfect Expansion Property (<strong>PEP</strong> and <strong>DPEP</strong>). This gives a direct combinatorial way of establishing the unique ergodicity of automorphism groups of Fraïssé classes, without having to use the probabilistic arguments in Angel et al. (2014).</div><div>We focus on the special case of <span><math><msub><mrow><mi>D</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span>, the class of complete, <span><math><mi>n</mi></math></span>-partite digraphs. Not all structures in this class have the <strong>PEP</strong> and we classify which structures have the stronger <strong>DPEP</strong>. The structures with this expansion property are intimately connected with the definable geometric structure of a Fraïssé structure.</div><div>We also look at the <strong>PEP</strong> for semigeneric digraphs, but we do not settle the question of unique ergodicity of the automorphism group of the semigeneric digraph.<span><span><sup>1</sup></span></span> Surprisingly, there are non-trivial substructures of the semigeneric digraph with the <strong>PEP</strong>.</div></div>","PeriodicalId":50490,"journal":{"name":"European Journal of Combinatorics","volume":"132 ","pages":"Article 104265"},"PeriodicalIF":0.9,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145624162","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

Borel sets of Rado graphs and Ramsey’s theorem Rado图的Borel集与Ramsey定理

IF 0.9 3区数学

European Journal of Combinatorics Pub Date : 2026-02-01 Epub Date: 2025-10-13 DOI: 10.1016/j.ejc.2025.104260

Natasha Dobrinen

{"title":"Borel sets of Rado graphs and Ramsey’s theorem","authors":"Natasha Dobrinen","doi":"10.1016/j.ejc.2025.104260","DOIUrl":"10.1016/j.ejc.2025.104260","url":null,"abstract":"<div><div>The well-known Galvin-Prikry Theorem (Galvin and Prikry, 1973) states that Borel subsets of the Baire space are Ramsey: Given any Borel subset <span><math><mrow><mi>X</mi><mo>⊆</mo><msup><mrow><mrow><mo>[</mo><mi>ω</mi><mo>]</mo></mrow></mrow><mrow><mi>ω</mi></mrow></msup></mrow></math></span>, where <span><math><msup><mrow><mrow><mo>[</mo><mi>ω</mi><mo>]</mo></mrow></mrow><mrow><mi>ω</mi></mrow></msup></math></span> is endowed with the metric topology, each infinite subset <span><math><mrow><mi>X</mi><mo>⊆</mo><mi>ω</mi></mrow></math></span> contains an infinite subset <span><math><mrow><mi>Y</mi><mo>⊆</mo><mi>X</mi></mrow></math></span> such that <span><math><msup><mrow><mrow><mo>[</mo><mi>Y</mi><mo>]</mo></mrow></mrow><mrow><mi>ω</mi></mrow></msup></math></span> is either contained in <span><math><mi>X</mi></math></span> or disjoint from <span><math><mi>X</mi></math></span>. Kechris, Pestov, and Todorcevic point out in Kechris et al. (2005) the dearth of similar results for homogeneous structures. Such results are a necessary step to the larger goal of finding a correspondence between structures with infinite dimensional Ramsey properties and topological dynamics, extending their correspondence between the Ramsey property and extreme amenability. In this article, we prove an analogue of the Galvin-Prikry theorem for the Rado graph. Any such infinite dimensional Ramsey theorem is subject to constraints following from work in Laflamme (2006). The proof uses techniques developed for the author’s work on the Ramsey theory of the Henson graphs (Dobrinen, 2020 and Dobrinen, 2023) as well as some new methods for fusion sequences, used to bypass the lack of a certain amalgamation property enjoyed by the Baire space.</div></div>","PeriodicalId":50490,"journal":{"name":"European Journal of Combinatorics","volume":"132 ","pages":"Article 104260"},"PeriodicalIF":0.9,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145623513","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

Topological dynamics of Polish group extensions 波兰群扩展的拓扑动力学

IF 0.9 3区数学

European Journal of Combinatorics Pub Date : 2026-02-01 Epub Date: 2025-10-16 DOI: 10.1016/j.ejc.2025.104263

Colin Jahel , Andy Zucker

引用次数: 0

First order logic and twin-width in tournaments and dense oriented graphs 竞赛图和密集面向图中的一阶逻辑和双宽度

IF 0.9 3区数学

European Journal of Combinatorics Pub Date : 2026-02-01 Epub Date: 2025-10-10 DOI: 10.1016/j.ejc.2025.104247

Colin Geniet , Stéphan Thomassé

{"title":"First order logic and twin-width in tournaments and dense oriented graphs","authors":"Colin Geniet , Stéphan Thomassé","doi":"10.1016/j.ejc.2025.104247","DOIUrl":"10.1016/j.ejc.2025.104247","url":null,"abstract":"<div><div>We characterise the classes of tournaments with tractable first-order model checking. For every hereditary class of tournaments <span><math><mi>T</mi></math></span>, first-order model checking is either fixed parameter tractable or <span><math><mrow><mtext>AW</mtext><mrow><mo>[</mo><mo>∗</mo><mo>]</mo></mrow></mrow></math></span>-hard. This dichotomy coincides with the fact that <span><math><mi>T</mi></math></span> has either bounded or unbounded twin-width, and that the growth of <span><math><mi>T</mi></math></span> is either at most exponential or at least factorial. From the model-theoretic point of view, we show that NIP classes of tournaments coincide with bounded twin-width. Twin-width is also characterised by three infinite families of obstructions: <span><math><mi>T</mi></math></span> has bounded twin-width if and only if it excludes at least one tournament from each family. This generalises results of Bonnet et al. on ordered graphs.</div><div>The key for these results is a polynomial time algorithm that takes as input a tournament <span><math><mi>T</mi></math></span> and computes a linear order <span><math><mo><</mo></math></span> on <span><math><mrow><mi>V</mi><mrow><mo>(</mo><mi>T</mi><mo>)</mo></mrow></mrow></math></span> such that the twin-width of the birelation <span><math><mrow><mo>(</mo><mi>T</mi><mo>,</mo><mo><</mo><mo>)</mo></mrow></math></span> is at most some function of the twin-width of <span><math><mi>T</mi></math></span>. Since approximating twin-width can be done in polynomial time for an ordered structure <span><math><mrow><mo>(</mo><mi>T</mi><mo>,</mo><mo><</mo><mo>)</mo></mrow></math></span>, this provides a polynomial time approximation of twin-width for tournaments.</div><div>Our results extend to oriented graphs with stable sets of bounded size, which may also be augmented by arbitrary binary relations.</div></div>","PeriodicalId":50490,"journal":{"name":"European Journal of Combinatorics","volume":"132 ","pages":"Article 104247"},"PeriodicalIF":0.9,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145247904","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

Reconfiguring homomorphisms to reflexive graphs via a simple reduction 通过简单的约简将同态重新配置为自反图

IF 0.9 3区数学

European Journal of Combinatorics Pub Date : 2026-02-01 Epub Date: 2025-10-15 DOI: 10.1016/j.ejc.2025.104251

Moritz Mühlenthaler , Mark Siggers , Thomas Suzan

{"title":"Reconfiguring homomorphisms to reflexive graphs via a simple reduction","authors":"Moritz Mühlenthaler , Mark Siggers , Thomas Suzan","doi":"10.1016/j.ejc.2025.104251","DOIUrl":"10.1016/j.ejc.2025.104251","url":null,"abstract":"<div><div>Given a graph <span><math><mi>G</mi></math></span> and two graph homomorphisms <span><math><mi>α</mi></math></span> and <span><math><mi>β</mi></math></span> from <span><math><mi>G</mi></math></span> to a fixed graph <span><math><mi>H</mi></math></span>, the problem <span><math><mi>H</mi></math></span>-recoloring asks whether there is a transformation from <span><math><mi>α</mi></math></span> to <span><math><mi>β</mi></math></span> that changes the image of a single vertex at each step and keeps a graph homomorphism throughout. The complexity of the problem depends, among other things, on the presence of loops on the vertices. We provide a simple reduction that, using a known algorithmic result for <span><math><mi>H</mi></math></span>-recoloring for square-free irreflexive graphs <span><math><mi>H</mi></math></span>, yields a polynomial-time algorithm for <span><math><mi>H</mi></math></span>-recoloring for square-free reflexive graphs <span><math><mi>H</mi></math></span>. This generalizes all known algorithmic results for <span><math><mi>H</mi></math></span>-recoloring for reflexive graphs <span><math><mi>H</mi></math></span>. Furthermore, the construction allows us to reprove some of the known hardness results. Finally, we provide a partial inverse of the construction for bipartite instances.</div></div>","PeriodicalId":50490,"journal":{"name":"European Journal of Combinatorics","volume":"132 ","pages":"Article 104251"},"PeriodicalIF":0.9,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145326851","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

Quasi-fixed points of substitutive systems 替代系统的拟不动点

IF 0.9 3区数学

European Journal of Combinatorics Pub Date : 2026-02-01 Epub Date: 2025-11-08 DOI: 10.1016/j.ejc.2025.104282

Elżbieta Krawczyk

引用次数: 0

Note on a problem of Sárközy on multiplicative representation functions 关于乘法表示函数Sárközy问题的说明

IF 0.9 3区数学

European Journal of Combinatorics Pub Date : 2026-02-01 Epub Date: 2025-10-15 DOI: 10.1016/j.ejc.2025.104268

Yuchen Ding

引用次数: 0

A variant of the Erdős–Gyárfás problem for K8 K8的Erdős-Gyárfás问题的一个变体