发布求助
文献互助 智能选刊 最新文献

Ars Mathematica Contemporanea最新文献

筛选
英文 中文
Answers to questions about medial layer graphs of self-dual regular and chiral polytopes 有关自偶正则和手性多面体中间层图的问题解答
IF 0.8 3区 数学
Ars Mathematica Contemporanea Pub Date : 2023-12-15 DOI: 10.26493/1855-3974.3229.8b1
M. Conder, Isabelle Steinmann
{"title":"Answers to questions about medial layer graphs of self-dual regular and chiral polytopes","authors":"M. Conder, Isabelle Steinmann","doi":"10.26493/1855-3974.3229.8b1","DOIUrl":"https://doi.org/10.26493/1855-3974.3229.8b1","url":null,"abstract":"","PeriodicalId":49239,"journal":{"name":"Ars Mathematica Contemporanea","volume":"11 3","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138998433","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
On the metric subgraphs of a graph 在图的度量子图上
3区 数学
Ars Mathematica Contemporanea Pub Date : 2023-11-08 DOI: 10.26493/1855-3974.2992.a6d
Yanan Hu, Xingzhi Zhan
{"title":"On the metric subgraphs of a graph","authors":"Yanan Hu, Xingzhi Zhan","doi":"10.26493/1855-3974.2992.a6d","DOIUrl":"https://doi.org/10.26493/1855-3974.2992.a6d","url":null,"abstract":"The three subgraphs of a connected graph induced by the center, annulus and periphery are called its metric subgraphs. The main results are as follows. (1) There exists a graph of order n whose metric subgraphs are all paths if and only if n ≥ 13 and the smallest size of such a graph of order 13 is 22; (2) there exists a graph of order n whose metric subgraphs are all cycles if and only if n ≥ 15, and there are exactly three such graphs of order 15; (3) for every integer k ≥ 3, we determine the possible orders for the existence of a graph whose metric subgraphs are all connected k-regular graphs; (4) there exists a graph of order n whose metric subgraphs are connected and pairwise isomorphic if and only if n ≥ 24 and n is divisible by 3. An unsolved problem is posed.","PeriodicalId":49239,"journal":{"name":"Ars Mathematica Contemporanea","volume":"135 3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135342368","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
Generalized Cayley maps and their Petrie duals 广义Cayley映射及其Petrie对偶
3区 数学
Ars Mathematica Contemporanea Pub Date : 2023-11-06 DOI: 10.26493/1855-3974.2408.42e
Robert Jajcay, Jozef Širáň, Yan Wang
{"title":"Generalized Cayley maps and their Petrie duals","authors":"Robert Jajcay, Jozef Širáň, Yan Wang","doi":"10.26493/1855-3974.2408.42e","DOIUrl":"https://doi.org/10.26493/1855-3974.2408.42e","url":null,"abstract":"Cayley maps are embeddings of Cayley graphs in orientable surfaces which possess a group of orientation preserving automorphisms acting regularly on the vertices. We generalize the concept of a Cayley map by considering embeddings of Cayley graphs in both orientable and non-orientable surfaces and by requiring a group of automorphisms acting regularly on vertices that does not have to consist entirely of orientation preserving automorphisms. This leads to new families of maps in both the orientable and non-orientable cases. Since the Petrie dual operator preserves the property of being a generalized Cayley map, throughout the paper we consider the action of this operator on our maps.","PeriodicalId":49239,"journal":{"name":"Ars Mathematica Contemporanea","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135633995","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
On the number of non-isomorphic (simple) k-gonal biembeddings of complete multipartite graphs 完全多部图的非同构(简单)k-角双嵌入的个数
3区 数学
Ars Mathematica Contemporanea Pub Date : 2023-10-26 DOI: 10.26493/1855-3974.2910.5b3
Simone Costa, Anita Pasotti
{"title":"On the number of non-isomorphic (simple) k-gonal biembeddings of complete multipartite graphs","authors":"Simone Costa, Anita Pasotti","doi":"10.26493/1855-3974.2910.5b3","DOIUrl":"https://doi.org/10.26493/1855-3974.2910.5b3","url":null,"abstract":"This article aims to provide exponential lower bounds on the number of non-isomorphic k-gonal face-2-colourable embeddings (sometimes called, with abuse of notation, biembeddings) of the complete multipartite graph into orientable surfaces. For this purpose, we use the concept, introduced by Archdeacon in 2015, of Heffer array and its relations with graph embeddings. In particular we show that, under certain hypotheses, from a single Heffter array, we can obtain an exponential number of distinct graph embeddings. Exploiting this idea starting from the arrays constructed by Cavenagh, Donovan and Yazıcı in 2020, we obtain that, for infinitely many values of k and v, there are at least kk/2 + o(k) ⋅ 2v ⋅ H(1/4)/(2k)^2 + o(v) non-isomorphic k-gonal face-2-colourable embeddings of Kv, where H(⋅) is the binary entropy. Moreover about the embeddings of Kv/t × t, for t ∈ {1, 2, k}, we provide a construction of 2v ⋅ H(1/4)/2k(k−1) + o(v,k) non-isomorphic k-gonal face-2-colourable embeddings whenever k is odd and v belongs to a wide infinite family of values.","PeriodicalId":49239,"journal":{"name":"Ars Mathematica Contemporanea","volume":"14 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136377025","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: 4
Complete resolution of the circulant nut graph order–degree existence problem 完全解决了循环螺母图的有序度存在性问题
3区 数学
Ars Mathematica Contemporanea Pub Date : 2023-10-23 DOI: 10.26493/1855-3974.3009.6df
Ivan Damnjanović
{"title":"Complete resolution of the circulant nut graph order–degree existence problem","authors":"Ivan Damnjanović","doi":"10.26493/1855-3974.3009.6df","DOIUrl":"https://doi.org/10.26493/1855-3974.3009.6df","url":null,"abstract":"A circulant nut graph is a non-trivial simple graph such that its adjacency matrix is a circulant matrix whose null space is spanned by a single vector without zero elements. Regarding these graphs, the order–degree existence problem can be thought of as the mathematical problem of determining all the possible pairs (n, d) for which there exists a d-regular circulant nut graph of order n. This problem was initiated by Bašić et al. and the first major results were obtained by Damnjanović and Stevanović, who proved that for each odd t ≥ 3 such that t ≢10 1 and t ≢18 15, there exists a 4t-regular circulant nut graph of order n for each even n ≥ 4t + 4. Afterwards, Damnjanović improved these results by showing that there necessarily exists a 4t-regular circulant nut graph of order n whenever t is odd, n is even, and n ≥ 4t + 4 holds, or whenever t is even, n is such that n ≡4 2, and n ≥ 4t + 6 holds. In this paper, we extend the aforementioned results by completely resolving the circulant nut graph order–degree existence problem. In other words, we fully determine all the possible pairs (n, d) for which there exists a d-regular circulant nut graph of order n.","PeriodicalId":49239,"journal":{"name":"Ars Mathematica Contemporanea","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135406284","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: 3
Connected Turán number of trees 连接Turán树的数量
3区 数学
Ars Mathematica Contemporanea Pub Date : 2023-10-03 DOI: 10.26493/1855-3974.3109.e4b
Yair Caro, Balázs Patkós, Zsolt Tuza
{"title":"Connected Turán number of trees","authors":"Yair Caro, Balázs Patkós, Zsolt Tuza","doi":"10.26493/1855-3974.3109.e4b","DOIUrl":"https://doi.org/10.26493/1855-3974.3109.e4b","url":null,"abstract":"The connected Turán number is a variant of the much studied Turán number, ex(n,F), the largest number of edges that an n-vertex F-free graph may contain. We start a systematic study of the connected Turán number exc(n,F), the largest number of edges that an n-vertex connected F-free graph may contain. We focus on the case where the forbidden graph is a tree. Prior to our work, exc(n,T) was determined only for the case T is a star or a path. Our main contribution is the determination of the exact value of exc(n,T) for small trees, in particular for all trees with at most six vertices, as well as some trees on seven vertices and several infinite families of trees. We also collect several lower-bound constructions of connected T-free graphs based on different graph parameters. The celebrated conjecture of Erdős and Sós states that for any tree T, we have ex(n,T) ≤ (|T|−2)n/2. We address the problem how much smaller exc(n,T) can be, what is the smallest possible ratio of exc(n,T) and (|T|−2)n/2 as |T| grows.","PeriodicalId":49239,"journal":{"name":"Ars Mathematica Contemporanea","volume":"46 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135738955","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
Generalized X-join of graphs and their automorphisms 图的广义x联接及其自同构
3区 数学
Ars Mathematica Contemporanea Pub Date : 2023-09-27 DOI: 10.26493/1855-3974.2619.06c
Javad Bagherian, Hanieh Memarzadeh
{"title":"Generalized X-join of graphs and their automorphisms","authors":"Javad Bagherian, Hanieh Memarzadeh","doi":"10.26493/1855-3974.2619.06c","DOIUrl":"https://doi.org/10.26493/1855-3974.2619.06c","url":null,"abstract":"In this paper, we first introduce a new product of finite graphs as a generalization of the X-join of graphs. We then give the necessary and sufficient conditions under which a graph has the generalized X-join structure. As a main result, we compute the full automorphism groups of the family of graphs that have the generalized X-join structure.","PeriodicalId":49239,"journal":{"name":"Ars Mathematica Contemporanea","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135476074","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
Vertex numbers of simplicial complexes with free abelian fundamental group 具有自由阿贝尔基本群的简单复形的顶点数
3区 数学
Ars Mathematica Contemporanea Pub Date : 2023-09-26 DOI: 10.26493/1855-3974.3089.b49
Florian Frick, Matt Superdock
{"title":"Vertex numbers of simplicial complexes with free abelian fundamental group","authors":"Florian Frick, Matt Superdock","doi":"10.26493/1855-3974.3089.b49","DOIUrl":"https://doi.org/10.26493/1855-3974.3089.b49","url":null,"abstract":"We show that the minimum number of vertices of a simplicial complex with fundamental group ℤn is at most O(n) and at least Ω(n3/4). For the upper bound, we use a result on orthogonal 1-factorizations of K2n. For the lower bound, we use a fractional Sylvester–Gallai result. This application of extremal results in discrete geometry seems to be new. We also prove that any group presentation ⟨S|R⟩ ≅ ℤn whose relations are of the form gahbic for g, h, i ∈ S has at least Ω(n3/2) generators.","PeriodicalId":49239,"journal":{"name":"Ars Mathematica Contemporanea","volume":"36 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134903229","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: 2
Edge-transitive core-free Nest graphs 无核边缘传递的巢图
3区 数学
Ars Mathematica Contemporanea Pub Date : 2023-09-15 DOI: 10.26493/1855-3974.2944.9cd
István Kovács
{"title":"Edge-transitive core-free Nest graphs","authors":"István Kovács","doi":"10.26493/1855-3974.2944.9cd","DOIUrl":"https://doi.org/10.26493/1855-3974.2944.9cd","url":null,"abstract":"A finite simple graph Γ is called a Nest graph if it is regular of valency 6 and admits an automorphism ρ with two orbits of the same length such that at least one of the subgraphs induced by these orbits is a cycle. We say that Γ is core-free if no non-trivial subgroup of the group generated by ρ is normal in Aut(Γ). In this paper, we show that, if Γ is edge-transitive and core-free, then it is isomorphic to one of the following graphs: the complement of the Petersen graph, the Hamming graph H(2,4), the Shrikhande graph and a certain normal 2-cover of K3, 3 by ℤ24.","PeriodicalId":49239,"journal":{"name":"Ars Mathematica Contemporanea","volume":"54 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135437320","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: 1
Ehrhart limits
IF 0.8 3区 数学
Ars Mathematica Contemporanea Pub Date : 2023-08-11 DOI: 10.26493/1855-3974.3092.4af
Benjamin Braun, McCabe Olsen
{"title":"Ehrhart limits","authors":"Benjamin Braun, McCabe Olsen","doi":"10.26493/1855-3974.3092.4af","DOIUrl":"https://doi.org/10.26493/1855-3974.3092.4af","url":null,"abstract":"","PeriodicalId":49239,"journal":{"name":"Ars Mathematica Contemporanea","volume":"20 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84131920","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
下一页 尾页
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整，为了账户安全，请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们：info@booksci.cn Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号：481959085
Book学术官方微信