Combinatorica最新文献_第4页

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

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

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

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

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

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":"Reidl et al. (Eur J Comb 75:152–168, 2019) characterized graph classes of bounded expansion as follows: A class ({mathcal {C}}) closed under subgraphs has bounded expansion if and only if there exists a function (f:{mathbb {N}} rightarrow {mathbb {N}}) such that for every graph (G in {mathcal {C}}), every nonempty subset A of vertices in G and every nonnegative integer r, the number of distinct intersections between A and a ball of radius r in G is at most f(r) |A|. When ({mathcal {C}}) has bounded expansion, the function f(r) 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 f(r) could be taken to be a polynomial. In this paper, we prove this conjecture: For every nonempty subset A of vertices in a planar graph G and every nonnegative integer r, the number of distinct intersections between A and a ball of radius r in G is ({{,mathrm{{mathcal {O}}},}}(r^4 |A|)). We also show that a polynomial bound holds more generally for every proper minor-closed class of graphs.\u0000","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

List-Avoiding Orientations 避免列表定向

IF 1.1 2区数学

Combinatorica Pub Date : 2024-06-11 DOI: 10.1007/s00493-024-00109-z

Peter Bradshaw, Yaobin Chen, Hao Ma, Bojan Mohar, Hehui Wu

引用次数: 0

Arc Connectivity and Submodular Flows in Digraphs 数图中的弧连接和次模流

IF 1.1 2区数学

Combinatorica Pub Date : 2024-05-28 DOI: 10.1007/s00493-024-00108-0

Ahmad Abdi, Gérard Cornuéjols, Giacomo Zambelli

{"title":"Arc Connectivity and Submodular Flows in Digraphs","authors":"Ahmad Abdi, Gérard Cornuéjols, Giacomo Zambelli","doi":"10.1007/s00493-024-00108-0","DOIUrl":"https://doi.org/10.1007/s00493-024-00108-0","url":null,"abstract":"Let (D=(V,A)) be a digraph. For an integer (kge 1), a k-arc-connected flip is an arc subset of D such that after reversing the arcs in it the digraph becomes (strongly) k-arc-connected. The first main result of this paper introduces a sufficient condition for the existence of a k-arc-connected flip that is also a submodular flow for a crossing submodular function. More specifically, given some integer (tau ge 1), suppose (d_A^+(U)+(frac{tau }{k}-1)d_A^-(U)ge tau ) for all (Usubsetneq V, Une emptyset ), where (d_A^+(U)) and (d_A^-(U)) denote the number of arcs in A leaving and entering U, respectively. Let ({mathcal {C}}) be a crossing family over ground set V, and let (f:{mathcal {C}}rightarrow {mathbb {Z}}) be a crossing submodular function such that (f(U)ge frac{k}{tau }(d_A^+(U)-d_A^-(U))) for all (Uin {mathcal {C}}). Then D has a k-arc-connected flip J such that (f(U)ge d_J^+(U)-d_J^-(U)) for all (Uin {mathcal {C}}). The result has several applications to Graph Orientations and Combinatorial Optimization. In particular, it strengthens Nash-Williams’ so-called weak orientation theorem, and proves a weaker variant of Woodall’s conjecture on digraphs whose underlying undirected graph is (tau )-edge-connected. The second main result of this paper is even more general. It introduces a sufficient condition for the existence of capacitated integral solutions to the intersection of two submodular flow systems. This sufficient condition implies the classic result of Edmonds and Giles on the box-total dual integrality of a submodular flow system. It also has the consequence that in a weakly connected digraph, the intersection of two submodular flow systems is totally dual integral.","PeriodicalId":50666,"journal":{"name":"Combinatorica","volume":"29 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141159422","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

Effective Bounds for Induced Size-Ramsey Numbers of Cycles 诱导大小拉姆齐循环数的有效界限

IF 1.1 2区数学

Combinatorica Pub Date : 2024-05-14 DOI: 10.1007/s00493-024-00103-5

Domagoj Bradač, Nemanja Draganić, Benny Sudakov

{"title":"Effective Bounds for Induced Size-Ramsey Numbers of Cycles","authors":"Domagoj Bradač, Nemanja Draganić, Benny Sudakov","doi":"10.1007/s00493-024-00103-5","DOIUrl":"https://doi.org/10.1007/s00493-024-00103-5","url":null,"abstract":"The induced size-Ramsey number (hat{r}_text {ind}^k(H)) of a graph H is the smallest number of edges a (host) graph G can have such that for any k-coloring of its edges, there exists a monochromatic copy of H which is an induced subgraph of G. In 1995, in their seminal paper, Haxell, Kohayakawa and Łuczak showed that for cycles, these numbers are linear for any constant number of colours, i.e., (hat{r}_text {ind}^k(C_n)le Cn) for some (C=C(k)). The constant C comes from the use of the regularity lemma, and has a tower type dependence on k. In this paper we significantly improve these bounds, showing that (hat{r}_text {ind}^k(C_n)le O(k^{102})n) when n is even, thus obtaining only a polynomial dependence of C on k. We also prove (hat{r}_text {ind}^k(C_n)le e^{O(klog k)}n) for odd n, which almost matches the lower bound of (e^{Omega (k)}n). Finally, we show that the ordinary (non-induced) size-Ramsey number satisfies (hat{r}^k(C_n)=e^{O(k)}n) for odd n. This substantially improves the best previous result of (e^{O(k^2)}n), and is best possible, up to the implied constant in the exponent. To achieve our results, we present a new host graph construction which, roughly speaking, reduces our task to finding a cycle of approximate given length in a graph with local sparsity.","PeriodicalId":50666,"journal":{"name":"Combinatorica","volume":"67 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140919474","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 Proof of a Frankl–Kupavskii Conjecture on Intersecting Families 弗兰克尔-库帕夫斯基相交族猜想的证明

IF 1.1 2区数学

Combinatorica Pub Date : 2024-05-14 DOI: 10.1007/s00493-024-00105-3

Agnijo Banerjee

引用次数: 0