Annals of Combinatorics最新文献_第2页

Extremal Totally Regular Mixed Graphs and Partially Oriented Incidence Graphs of Projective and Biaffine Planes 射影平面和双仿平面的极值全正则混合图和部分定向关联图

IF 0.8 4区数学

Annals of Combinatorics Pub Date : 2025-11-03 DOI: 10.1007/s00026-025-00788-5

Tatiana B. Jajcayová, Robert Jajcay, György Kiss, István Porupsánszki

{"title":"Extremal Totally Regular Mixed Graphs and Partially Oriented Incidence Graphs of Projective and Biaffine Planes","authors":"Tatiana B. Jajcayová, Robert Jajcay, György Kiss, István Porupsánszki","doi":"10.1007/s00026-025-00788-5","DOIUrl":"10.1007/s00026-025-00788-5","url":null,"abstract":"<div>An (r, z; g)-mixed graph is a graph containing both edges and darts satisfying the regularity property that each vertex of the graph is incident to r edges, z ingoing and z outgoing darts (called total regularity), and being of oriented girth g, i.e., containing an oriented cycle of length g, and no shorter oriented cycles. The problem addressed in this paper is analogous to the Cage Problem and calls for determining the orders of the smallest totally regular (r, z; g)-mixed graphs. We derive several upper and lower bounds on the orders of such minimal graphs, study the relations between these extremal graphs and their non-oriented or digraphical counterparts, and focus on properties of totally regular mixed graphs obtained by replacing some of the edges of the incidence graphs of projective and biaffine planes by darts. We also introduce two constructions based on introducing additional edges or darts into induced subgraphs of these incidence graphs.</div>","PeriodicalId":50769,"journal":{"name":"Annals of Combinatorics","volume":"30 3","pages":"797 - 815"},"PeriodicalIF":0.8,"publicationDate":"2025-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00026-025-00788-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149007371","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Spectral Analysis of Normalized Hermitian Laplacian Matrices in Random Mixed Graphs 随机混合图中归一化厄米拉普拉斯矩阵的谱分析

IF 0.8 4区数学

Annals of Combinatorics Pub Date : 2025-11-02 DOI: 10.1007/s00026-025-00786-7

Dan Hu, Hajo Broersma, Xueliang Li, Shenggui Zhang

引用次数: 0

On Paths with Three Blocks of the Form P(1, k, 1) in Digraphs 有向图中P（1, k, 1）形式的三块路径

IF 0.8 4区数学

Annals of Combinatorics Pub Date : 2025-10-31 DOI: 10.1007/s00026-025-00789-4

Maidoun Mortada, Amin El Sahili, Zahraa Mohsen

引用次数: 0

On the Asymptotics of Certain Colored Partitions 关于某些有色分区的渐近性

IF 0.7 4区数学

Annals of Combinatorics Pub Date : 2025-10-08 DOI: 10.1007/s00026-025-00771-0

Lukas Mauth

引用次数: 0

Enumeration of Pattern-Avoiding Alternating Sign Matrices: An Asymptotic Dichotomy 避免模式的交替符号矩阵的枚举：一个渐近二分法

IF 0.7 4区数学

Annals of Combinatorics Pub Date : 2025-09-20 DOI: 10.1007/s00026-025-00784-9

Mathilde Bouvel, Eric S. Egge, Rebecca N. Smith, Jessica Striker, Justin M. Troyka

引用次数: 0

Exploring the Closure Operator for Minimal a, b-Separators: Insights from Galois Connections 探索极小a， b分隔符的闭包算子：来自伽罗瓦连接的见解

IF 0.8 4区数学

Annals of Combinatorics Pub Date : 2025-09-03 DOI: 10.1007/s00026-025-00781-y

Kohei Nomura, Koichi Yamazaki

{"title":"Exploring the Closure Operator for Minimal a, b-Separators: Insights from Galois Connections","authors":"Kohei Nomura, Koichi Yamazaki","doi":"10.1007/s00026-025-00781-y","DOIUrl":"10.1007/s00026-025-00781-y","url":null,"abstract":"<div>Graph algorithms are important for many applications, and studying minimal separators is key to designing efficient graph algorithms. This paper examines minimal a, b-separators in graphs, looking at them from both graph theory and algebraic perspectives, with a focus on lattice theory. It is well known that the set (mathscr {M}_{ab}) of minimal a, b-separators of a graph forms a complete lattice. Since any lattice is isomorphic to the lattice of closed sets of a closure operator, a natural question arises: from which closure operator and poset can the lattice (mathscr {M}_{ab}) be obtained? We propose such a closure operator and poset. To this end, we make use of a carefully defined Galois connection. Galois connections naturally appear in lattice theory. To demonstrate our findings, we introduce two types of functions, NC and CN, which form the basis of the closure operator. NC-type functions are closely associated with full components, a concept that frequently appears in graph theoretical studies on minimal a, b-separators. On the other hand, CN-type functions are naturally associated with Galois connections. NC-type and CN-type functions are interrelated, and this interrelation reflects the fusion of graph theoretical and lattice theoretical approaches in this study.</div>","PeriodicalId":50769,"journal":{"name":"Annals of Combinatorics","volume":"30 3","pages":"635 - 653"},"PeriodicalIF":0.8,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00026-025-00781-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149007369","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

On Chip-Firing on Undirected Binary Trees 关于无向二叉树的芯片发射

IF 0.8 4区数学

Annals of Combinatorics Pub Date : 2025-08-18 DOI: 10.1007/s00026-025-00779-6

Ryota Inagaki, Tanya Khovanova, Austin Luo

引用次数: 0

Logarithmic Concavity of Bimatroids 双曲面的对数凹性

IF 0.8 4区数学

Annals of Combinatorics Pub Date : 2025-08-14 DOI: 10.1007/s00026-025-00780-z

Felix Röhrle, Martin Ulirsch

引用次数: 0

Graphs with Nonnegative Resistance Curvature 非负阻力曲率图

IF 0.8 4区数学

Annals of Combinatorics Pub Date : 2025-08-06 DOI: 10.1007/s00026-025-00774-x

Karel Devriendt

引用次数: 0

Bounds for the Independence and Chromatic Numbers of Locally Sparse Graphs 局部稀疏图的独立性和色数的界

IF 0.8 4区数学

Annals of Combinatorics Pub Date : 2025-08-05 DOI: 10.1007/s00026-025-00778-7

Abhishek Dhawan

{"title":"Bounds for the Independence and Chromatic Numbers of Locally Sparse Graphs","authors":"Abhishek Dhawan","doi":"10.1007/s00026-025-00778-7","DOIUrl":"10.1007/s00026-025-00778-7","url":null,"abstract":"<div>In this note, we consider a more general version of local sparsity introduced recently by Anderson, Kuchukova, and the author. In particular, we say a graph (G = (V, E)) is (k, r)-locally sparse if, for each vertex (v in V(G)), the subgraph induced by its neighborhood contains at most k cliques of size r. For (r geqslant 3) and (varepsilon in [0, 1]), we show that an n-vertex ((Delta ^{varepsilon r}, r))-locally sparse graph G of maximum degree (Delta ) satisfies (alpha (G) geqslant (1-o(1))dfrac{n}{eta Delta }) and (chi (G) leqslant Theta left( eta Delta right) ), where (eta :==varepsilon + dfrac{rlog log Delta }{log Delta }). For (varepsilon ) not too large, the hidden constant in the (Theta (cdot )) can be taken to be (1+o(1)). Setting (varepsilon = 0), we recover classical results on (K_{r+1})-free graphs due to Shearer and Johansson, which were more recently improved by Davies, Kang, Pirot, and Sereni. We prove a stronger result on the independence number in terms of the occupancy fraction in the hard-core model, and establish a local version of the coloring result in the more general setting of correspondence coloring.</div>","PeriodicalId":50769,"journal":{"name":"Annals of Combinatorics","volume":"30 2","pages":"277 - 304"},"PeriodicalIF":0.8,"publicationDate":"2025-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00026-025-00778-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148323469","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0