European Journal of Combinatorics最新文献_第10页

The semi-random tree process 半随机树过程

IF 1 3区数学

European Journal of Combinatorics Pub Date : 2025-01-28 DOI: 10.1016/j.ejc.2025.104120

Sofiya Burova , Lyuben Lichev

引用次数: 0

Building Hamiltonian cycles in the semi-random graph process in less than 2n rounds 在不到2n轮的半随机图过程中建立哈密顿环

IF 1 3区数学

European Journal of Combinatorics Pub Date : 2025-01-24 DOI: 10.1016/j.ejc.2025.104122

Alan Frieze , Pu Gao , Calum MacRury , Paweł Prałat , Gregory B. Sorkin

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引用次数: 0

Building graphs with high minimum degree on a budget 在预算上建立具有高最小度的图形

IF 1 3区数学

European Journal of Combinatorics Pub Date : 2025-01-24 DOI: 10.1016/j.ejc.2025.104119

Kyriakos Katsamaktsis , Shoham Letzter

{"title":"Building graphs with high minimum degree on a budget","authors":"Kyriakos Katsamaktsis , Shoham Letzter","doi":"10.1016/j.ejc.2025.104119","DOIUrl":"10.1016/j.ejc.2025.104119","url":null,"abstract":"<div><div>We consider the problem of constructing a graph of minimum degree <math><mrow><mi>k</mi><mo>≥</mo><mn>1</mn></mrow></math> in the following controlled random graph process, introduced recently by Frieze, Krivelevich and Michaeli. Suppose the edges of the complete graph on <math><mi>n</mi></math> vertices are permuted uniformly at random. A player, Builder, sees the edges one by one, and must decide irrevocably upon seeing each edge whether to add it to her graph (of already selected edges) or not. Suppose Builder decides to add an edge to her graph if and only if at least one endpoint has degree less than <math><mi>k</mi></math> in her graph. Frieze, Krivelevich and Michaeli observed that this strategy succeeds in building a graph of minimum degree at least <math><mi>k</mi></math> by <math><msub><mrow><mi>τ</mi></mrow><mrow><mi>k</mi></mrow></msub></math>, the hitting time for having minimum degree <math><mi>k</mi></math>. They conjectured that any strategy using <math><mrow><mi>ɛ</mi><mi>n</mi></mrow></math> fewer edges, where <math><mrow><mi>ɛ</mi><mo>></mo><mn>0</mn></mrow></math> is any constant, fails with high probability. In this paper we disprove their conjecture. We show that for <math><mrow><mi>k</mi><mo>≥</mo><mn>2</mn></mrow></math> Builder has a strategy which purchases <math><mrow><mi>n</mi><mo>/</mo><mn>9</mn></mrow></math> fewer edges and succeeds with high probability in building a graph of minimum degree at least <math><mi>k</mi></math> by <math><msub><mrow><mi>τ</mi></mrow><mrow><mi>k</mi></mrow></msub></math>. For <math><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow></math> we show that any strategy using <math><mrow><mi>ɛ</mi><mi>n</mi></mrow></math> fewer edges fails with probability bounded away from 0, and exhibit such a strategy that succeeds with probability bounded away from 0.</div></div>","PeriodicalId":50490,"journal":{"name":"European Journal of Combinatorics","volume":"129 ","pages":"Article 104119"},"PeriodicalIF":1.0,"publicationDate":"2025-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144588403","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

Non-geometric distance-regular graphs of diameter at least 3 with smallest eigenvalue at least −3 直径至少为3且最小特征值至少为- 3的非几何距离正则图

IF 1 3区数学

European Journal of Combinatorics Pub Date : 2025-01-18 DOI: 10.1016/j.ejc.2024.104118

Jack H. Koolen , Kefan Yu , Xiaoye Liang , Harrison Choi , Greg Markowsky

引用次数: 0

Visible lattice points in Pólya’s walks 在Pólya的行走中可见的点阵点

IF 1 3区数学

European Journal of Combinatorics Pub Date : 2025-01-16 DOI: 10.1016/j.ejc.2024.104116

Meijie Lu , Xianchang Meng

引用次数: 0

On naturally labelled posets and permutations avoiding 12–34 在自然标记的偏序集和排列上避免12-34

IF 1 3区数学

European Journal of Combinatorics Pub Date : 2025-01-13 DOI: 10.1016/j.ejc.2024.104117

David Bevan , Gi-Sang Cheon , Sergey Kitaev

引用次数: 0

On the maximum number of common neighbours in dense random regular graphs 稠密随机正则图中共同近邻的最大数目

IF 1 3区数学

European Journal of Combinatorics Pub Date : 2024-12-31 DOI: 10.1016/j.ejc.2024.104106

Mikhail Isaev , Maksim Zhukovskii

引用次数: 0

On heroes in digraphs with forbidden induced forests 论禁止诱导森林的有向图英雄

IF 1 3区数学

European Journal of Combinatorics Pub Date : 2024-12-26 DOI: 10.1016/j.ejc.2024.104104

Alvaro Carbonero , Hidde Koerts , Benjamin Moore , Sophie Spirkl

{"title":"On heroes in digraphs with forbidden induced forests","authors":"Alvaro Carbonero , Hidde Koerts , Benjamin Moore , Sophie Spirkl","doi":"10.1016/j.ejc.2024.104104","DOIUrl":"10.1016/j.ejc.2024.104104","url":null,"abstract":"<div><div>We continue a line of research which studies which hereditary families of digraphs have bounded dichromatic number. For a class of digraphs <math><mi>C</mi></math>, a hero in <math><mi>C</mi></math> is any digraph <math><mi>H</mi></math> such that <math><mi>H</mi></math>-free digraphs in <math><mi>C</mi></math> have bounded dichromatic number. We show that if <math><mi>F</mi></math> is an oriented star of degree at least five, the only heroes for the class of <math><mi>F</mi></math>-free digraphs are transitive tournaments. For oriented stars <math><mi>F</mi></math> of degree exactly four, we show the only heroes in <math><mi>F</mi></math>-free digraphs are transitive tournaments, or possibly special joins of transitive tournaments. Aboulker et al. characterized the set of heroes of <math><mrow><mo>{</mo><mi>H</mi><mo>,</mo><msub><mrow><mi>K</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>+</mo><mover><mrow><msub><mrow><mi>P</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow><mo>→</mo></mover><mo>}</mo></mrow></math>-free digraphs almost completely, and we show the same characterization for the class of <math><mrow><mo>{</mo><mi>H</mi><mo>,</mo><mi>r</mi><msub><mrow><mi>K</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>+</mo><mover><mrow><msub><mrow><mi>P</mi></mrow><mrow><mn>3</mn></mrow></msub></mrow><mo>→</mo></mover><mo>}</mo></mrow></math>-free digraphs. Lastly, we show that if we forbid two “valid” orientations of brooms, then every transitive tournament is a hero for this class of digraphs.</div></div>","PeriodicalId":50490,"journal":{"name":"European Journal of Combinatorics","volume":"125 ","pages":"Article 104104"},"PeriodicalIF":1.0,"publicationDate":"2024-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143136075","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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

A group action on cyclic compositions and γ-positivity 环组成与γ-正性的群作用

IF 1 3区数学

European Journal of Combinatorics Pub Date : 2024-12-20 DOI: 10.1016/j.ejc.2024.104107

Shishuo Fu , Jie Yang

{"title":"A group action on cyclic compositions and γ-positivity","authors":"Shishuo Fu , Jie Yang","doi":"10.1016/j.ejc.2024.104107","DOIUrl":"10.1016/j.ejc.2024.104107","url":null,"abstract":"<div><div>Let <math><msub><mrow><mi>w</mi></mrow><mrow><mi>n</mi><mo>,</mo><mi>k</mi><mo>,</mo><mi>m</mi></mrow></msub></math> be the number of Dyck paths of semilength <math><mi>n</mi></math> with <math><mi>k</mi></math> occurrences of <math><mrow><mi>U</mi><mi>D</mi></mrow></math> and <math><mi>m</mi></math> occurrences of <math><mrow><mi>U</mi><mi>U</mi><mi>D</mi></mrow></math>. We establish in two ways a new interpretation of the numbers <math><msub><mrow><mi>w</mi></mrow><mrow><mi>n</mi><mo>,</mo><mi>k</mi><mo>,</mo><mi>m</mi></mrow></msub></math> in terms of plane trees and internal nodes. The first way builds on a new characterization of plane trees that involves cyclic compositions. The second proof utilizes a known interpretation of <math><msub><mrow><mi>w</mi></mrow><mrow><mi>n</mi><mo>,</mo><mi>k</mi><mo>,</mo><mi>m</mi></mrow></msub></math> in terms of plane trees and leaves, and a recent involution on plane trees constructed by Li, Lin, and Zhao. Moreover, a group action on the set of cyclic compositions (or equivalently, 2-dominant compositions) is introduced, which amounts to give a combinatorial proof of the <math><mi>γ</mi></math>-positivity of the Narayana polynomial, as well as the <math><mi>γ</mi></math>-positivity of the polynomial <math><mrow><msub><mrow><mi>W</mi></mrow><mrow><mn>2</mn><mi>k</mi><mo>+</mo><mn>1</mn><mo>,</mo><mi>k</mi></mrow></msub><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>≔</mo><msub><mrow><mo>∑</mo></mrow><mrow><mn>1</mn><mo>≤</mo><mi>m</mi><mo>≤</mo><mi>k</mi></mrow></msub><msub><mrow><mi>w</mi></mrow><mrow><mn>2</mn><mi>k</mi><mo>+</mo><mn>1</mn><mo>,</mo><mi>k</mi><mo>,</mo><mi>m</mi></mrow></msub><msup><mrow><mi>t</mi></mrow><mrow><mi>m</mi></mrow></msup></mrow></math> previously obtained by Bóna et al, with apparently new combinatorial interpretations of their <math><mi>γ</mi></math>-coefficients.</div></div>","PeriodicalId":50490,"journal":{"name":"European Journal of Combinatorics","volume":"125 ","pages":"Article 104107"},"PeriodicalIF":1.0,"publicationDate":"2024-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143136446","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

Coloring minimal Cayley graphs 最小Cayley图的着色

IF 1 3区数学

European Journal of Combinatorics Pub Date : 2024-12-19 DOI: 10.1016/j.ejc.2024.104108

Ignacio García-Marco , Kolja Knauer

引用次数: 0