Combinatorics, Probability and Computing最新文献_第2页

Central limit theorem for components in meandric systems through high moments 通过高矩阵计算均方差系统成分的中心极限定理

Combinatorics, Probability and Computing Pub Date : 2024-04-29 DOI: 10.1017/s0963548324000117

Svante Janson, Paul Thévenin

引用次数: 0

Behaviour of the minimum degree throughout the -process 在整个过程中最低限度的行为

Combinatorics, Probability and Computing Pub Date : 2024-04-22 DOI: 10.1017/s0963548324000105

Jakob Hofstad

{"title":"Behaviour of the minimum degree throughout the -process","authors":"Jakob Hofstad","doi":"10.1017/s0963548324000105","DOIUrl":"https://doi.org/10.1017/s0963548324000105","url":null,"abstract":"The $d$ -process generates a graph at random by starting with an empty graph with $n$ vertices, then adding edges one at a time uniformly at random among all pairs of vertices which have degrees at most $d-1$ and are not mutually joined. We show that, in the evolution of a random graph with $n$ vertices under the $d$ -process with $d$ fixed, with high probability, for each $j in {0,1,dots,d-2}$ , the minimum degree jumps from $j$ to $j+1$ when the number of steps left is on the order of $ln (n)^{d-j-1}$ . This answer","PeriodicalId":10503,"journal":{"name":"Combinatorics, Probability and Computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140637454","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

A generalization of Bondy’s pancyclicity theorem 邦迪泛周期定理的一般化

Combinatorics, Probability and Computing Pub Date : 2024-04-17 DOI: 10.1017/s0963548324000075

Nemanja Draganić, David Munhá Correia, Benny Sudakov

引用次数: 0

The distribution of the maximum protection number in simply generated trees 简单生成树中最大保护数的分布

Combinatorics, Probability and Computing Pub Date : 2024-04-12 DOI: 10.1017/s0963548324000099

Clemens Heuberger, Sarah J. Selkirk, Stephan Wagner

{"title":"The distribution of the maximum protection number in simply generated trees","authors":"Clemens Heuberger, Sarah J. Selkirk, Stephan Wagner","doi":"10.1017/s0963548324000099","DOIUrl":"https://doi.org/10.1017/s0963548324000099","url":null,"abstract":"The protection number of a vertex $v$ in a tree is the length of the shortest path from $v$ to any leaf contained in the maximal subtree where $v$ is the root. In this paper, we determine the distribution of the maximum protection number of a vertex in simply generated trees, thereby refining a recent result of Devroye, Goh, and Zhao. Two different cases can be observed: if the given family of trees allows vertices of outdegree $1$ , then the maximum protection number is on average logarithmic in the tree size, with a discrete double-exponential limiting distribution. If no such vertices are allowed, the maximum protection number is doubly logarithmic in the tree size and concentrated on at most two values. These results are obtained by studying the singular behaviour of the generating functions of trees with bounded protection number. While a general distributional result by Prodinger and Wagner can be used in the first case, we prove a variant of that result in the second case.","PeriodicalId":10503,"journal":{"name":"Combinatorics, Probability and Computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140603332","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

Algorithms for the ferromagnetic Potts model on expanders 扩展器上铁磁波茨模型的算法

Combinatorics, Probability and Computing Pub Date : 2024-04-05 DOI: 10.1017/s0963548324000087

Charlie Carlson, Ewan Davies, Nicolas Fraiman, Alexandra Kolla, Aditya Potukuchi, Corrine Yap

{"title":"Algorithms for the ferromagnetic Potts model on expanders","authors":"Charlie Carlson, Ewan Davies, Nicolas Fraiman, Alexandra Kolla, Aditya Potukuchi, Corrine Yap","doi":"10.1017/s0963548324000087","DOIUrl":"https://doi.org/10.1017/s0963548324000087","url":null,"abstract":"We give algorithms for approximating the partition function of the ferromagnetic $q$ -color Potts model on graphs of maximum degree $d$ . Our primary contribution is a fully polynomial-time approximation scheme for $d$ -regular graphs with an expansion condition at low temperatures (that is, bounded away from the order-disorder threshold). The expansion condition is much weaker than in previous works; for example, the expansion exhibited by the hypercube suffices. The main improvements come from a significantly sharper analysis of standard polymer models; we use extremal graph theory and applications of Karger’s algorithm to count cuts that may be of independent interest. It is #BIS-hard to approximate the partition function at low temperatures on bounded-degree graphs, so our algorithm can be seen as evidence that hard instances of #BIS are rare. We also obtain efficient algorithms in the Gibbs uniqueness region for bounded-degree graphs. While our high-temperature proof follows more standard polymer model analysis, our result holds in the largest-known range of parameters $d$ and $q$ .","PeriodicalId":10503,"journal":{"name":"Combinatorics, Probability and Computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140575654","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

Antidirected subgraphs of oriented graphs 定向图的反向子图

Combinatorics, Probability and Computing Pub Date : 2024-03-06 DOI: 10.1017/s0963548324000038

Maya Stein, Camila Zárate-Guerén

引用次数: 0

A class of graphs of zero Turán density in a hypercube 超立方体中图兰密度为零的一类图形

Combinatorics, Probability and Computing Pub Date : 2024-03-05 DOI: 10.1017/s0963548324000063

Maria Axenovich

引用次数: 0

Sharp bounds for a discrete John’s theorem 离散约翰定理的锐界

Combinatorics, Probability and Computing Pub Date : 2024-03-05 DOI: 10.1017/s0963548324000051

Peter van Hintum, Peter Keevash

引用次数: 0

Large monochromatic components in expansive hypergraphs 扩张超图中的大型单色成分

Combinatorics, Probability and Computing Pub Date : 2024-03-05 DOI: 10.1017/s096354832400004x

Deepak Bal, Louis DeBiasio

引用次数: 0

Small subsets with large sumset: Beyond the Cauchy–Davenport bound 小子集与大和集：超越考奇-达文波特界限

Combinatorics, Probability and Computing Pub Date : 2024-02-21 DOI: 10.1017/s0963548324000014

Jacob Fox, Sammy Luo, Huy Tuan Pham, Yunkun Zhou

{"title":"Small subsets with large sumset: Beyond the Cauchy–Davenport bound","authors":"Jacob Fox, Sammy Luo, Huy Tuan Pham, Yunkun Zhou","doi":"10.1017/s0963548324000014","DOIUrl":"https://doi.org/10.1017/s0963548324000014","url":null,"abstract":"For a subset $A$ of an abelian group $G$ , given its size $|A|$ , its doubling $kappa =|A+A|/|A|$ , and a parameter $s$ which is small compared to $|A|$ , we study the size of the largest sumset $A+A'$ that can be guaranteed for a subset $A'$ of $A$ of size at most $s$ . We show that a subset $A'subseteq A$ </jats:alt","PeriodicalId":10503,"journal":{"name":"Combinatorics, Probability and Computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139924576","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