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Rainbow subgraphs in edge-colored planar and outerplanar graphs 边色平面和外平面图中的彩虹子图
IF 0.8
Discrete Mathematics Letters Pub Date : 2023-06-23 DOI: 10.47443/dml.2023.048
J. Czap
{"title":"Rainbow subgraphs in edge-colored planar and outerplanar graphs","authors":"J. Czap","doi":"10.47443/dml.2023.048","DOIUrl":"https://doi.org/10.47443/dml.2023.048","url":null,"abstract":"Let G be a class of graphs. The strong rainbow number of the graph H in G is the minimum number of colors k such that every graph G ∈ G admits an edge coloring with at most k colors in which all copies of H are rainbow (i","PeriodicalId":36023,"journal":{"name":"Discrete Mathematics Letters","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41943724","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
Odd Solutions to Systems of Inequalities Coming From Regular Chain Groups 正则链群不等式组的奇解
IF 0.8
Discrete Mathematics Letters Pub Date : 2023-06-20 DOI: 10.47443/dml.2023.033
Daniel C. Slilaty
{"title":"Odd Solutions to Systems of Inequalities Coming From Regular Chain Groups","authors":"Daniel C. Slilaty","doi":"10.47443/dml.2023.033","DOIUrl":"https://doi.org/10.47443/dml.2023.033","url":null,"abstract":"Hoffman’s theorem on feasible circulations and Ghouila-Houry’s theorem on feasible tensions are classical results of graph theory. Camion generalized these results to systems of inequalities over regular chain groups. An analogue of Camion’s result is proved in which solutions can be forced to be odd valued. The obtained result also generalizes the results of Pretzel and Youngs as well as Slilaty. It is also shown how Ghouila-Houry’s result can be used to give a new proof of the graph-coloring theorem of Minty and Vitaver.","PeriodicalId":36023,"journal":{"name":"Discrete Mathematics Letters","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45541239","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
The largest eigenvalue conditions for Hamiltonian and traceable graphs 哈密顿图和可迹图的最大特征值条件
IF 0.8
Discrete Mathematics Letters Pub Date : 2023-04-19 DOI: 10.47443/dml.2022.191
Rao Li
{"title":"The largest eigenvalue conditions for Hamiltonian and traceable graphs","authors":"Rao Li","doi":"10.47443/dml.2022.191","DOIUrl":"https://doi.org/10.47443/dml.2022.191","url":null,"abstract":"","PeriodicalId":36023,"journal":{"name":"Discrete Mathematics Letters","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43172209","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
On a Linear Combination of Zagreb Indices 关于Zagreb指数的线性组合
IF 0.8
Discrete Mathematics Letters Pub Date : 2023-04-10 DOI: 10.47443/dml.2023.029
A. Albalahi
{"title":"On a Linear Combination of Zagreb Indices","authors":"A. Albalahi","doi":"10.47443/dml.2023.029","DOIUrl":"https://doi.org/10.47443/dml.2023.029","url":null,"abstract":"The modified first Zagreb connection index of a triangle-free and quadrangle-free graph G is equal to 2 M 2 ( G ) − M 1 ( G ) , where M 2 ( G ) and M 1 ( G ) are the well-known second and first Zagreb indices of G , respectively. This paper involves the study of the linear combination 2 M 2 ( G ) − M 1 ( G ) of M 2 ( G ) and M 1 ( G ) when G is a connected graph of a given order and cyclomatic number. More precisely, graphs having the minimum value of the graph invariant 2 M 2 − M 1 are determined from the class of all connected graphs of order n and cyclomatic number c y , when c y ≥ 1 and n ≥ 2( c y − 1) .","PeriodicalId":36023,"journal":{"name":"Discrete Mathematics Letters","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49127719","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
On Boolean Functions Defined on Bracket Sequences 关于在括号序列上定义的布尔函数
IF 0.8
Discrete Mathematics Letters Pub Date : 2023-04-10 DOI: 10.47443/dml.2022.209
Norbert Hegyv´ari
{"title":"On Boolean Functions Defined on Bracket Sequences","authors":"Norbert Hegyv´ari","doi":"10.47443/dml.2022.209","DOIUrl":"https://doi.org/10.47443/dml.2022.209","url":null,"abstract":"In the paper [B. Bakos, N. Hegyv´ari, M. P´alfy, X. H. Yan, Discrete Math. Lett. 4 (2020) 31–36], the authors introduced the so-called pseudo-recursive sequences which generalize bracket sequences. In the present article, Boolean functions are defined on hypergraphs with edges having big intersections induced by bracket sequences and hypergraphs that are thinly intersecting. These Boolean functions related to combinatorial number theory are new in this area.","PeriodicalId":36023,"journal":{"name":"Discrete Mathematics Letters","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47901423","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
The Edge Partition Dimension of Graphs 图的边划分维数
IF 0.8
Discrete Mathematics Letters Pub Date : 2023-03-30 DOI: 10.47443/dml.2023.010
D. Kuziak, Elizabeth C. M. Maritz, Tom´aˇs Vetr´ık, I. Yero
{"title":"The Edge Partition Dimension of Graphs","authors":"D. Kuziak, Elizabeth C. M. Maritz, Tom´aˇs Vetr´ık, I. Yero","doi":"10.47443/dml.2023.010","DOIUrl":"https://doi.org/10.47443/dml.2023.010","url":null,"abstract":"The edge metric dimension was introduced in 2018 and since then, it has been extensively studied. In this paper, we present a different way to obtain resolving structures in graphs in order to gain more insight into the study of edge resolving sets and resolving partitions. We define the edge partition dimension of a connected graph and bound it for graphs of given order and for graphs with given maximum degree. We obtain exact values of the edge partition dimension for multipartite graphs. Some relations between the edge partition dimension and partition dimension/edge metric dimension are also presented. Moreover, several open problems for further research are stated.","PeriodicalId":36023,"journal":{"name":"Discrete Mathematics Letters","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45447877","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
An Optimal Lower Bound for the Size of Periodic Digraphs 周期有向图大小的最优下界
IF 0.8
Discrete Mathematics Letters Pub Date : 2023-03-28 DOI: 10.47443/dml.2023.015
S. Kozerenko
{"title":"An Optimal Lower Bound for the Size of Periodic Digraphs","authors":"S. Kozerenko","doi":"10.47443/dml.2023.015","DOIUrl":"https://doi.org/10.47443/dml.2023.015","url":null,"abstract":"A periodic digraph is the digraph associated with a periodic point of a continuous map from the unit interval to itself. This digraph encodes “covering” relation between minimal intervals in the corresponding orbit, which allows the application of purely combinatorial arguments in establishing results on the existence and co-existence of periods of periodic points (for example, in proving the famous Sharkovsky’s theorem). In this article, an optimal lower bound for the size of periodic digraphs is provided and thus some previous results of Pavlenko are tightened.","PeriodicalId":36023,"journal":{"name":"Discrete Mathematics Letters","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46949600","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
Some New Results on the Edge-Strength and Strength of Graphs 关于图的边强度和强度的一些新结果
IF 0.8
Discrete Mathematics Letters Pub Date : 2023-03-28 DOI: 10.47443/dml.2022.208
{"title":"Some New Results on the Edge-Strength and Strength of Graphs","authors":"","doi":"10.47443/dml.2022.208","DOIUrl":"https://doi.org/10.47443/dml.2022.208","url":null,"abstract":"","PeriodicalId":36023,"journal":{"name":"Discrete Mathematics Letters","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47125325","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: 2
Maximum Atom-Bond Sum-Connectivity Index of n-Order Trees With Fixed Number of Leaves 具有固定叶数的n阶树的最大原子键和连接性指数
IF 0.8
Discrete Mathematics Letters Pub Date : 2023-03-28 DOI: 10.47443/dml.2023.016
Sadia Noureen, Akbar Ali
{"title":"Maximum Atom-Bond Sum-Connectivity Index of n-Order Trees With Fixed Number of Leaves","authors":"Sadia Noureen, Akbar Ali","doi":"10.47443/dml.2023.016","DOIUrl":"https://doi.org/10.47443/dml.2023.016","url":null,"abstract":"Let G be a graph. For an edge e of G , denote by d e the number of edges adjacent to e . The atom-bond sum-connectivity (ABS) index of G is defined as ABS ( G ) = (cid:80) e ∈ E ( G ) (cid:112) 1 − 2( d e + 2) − 1 . A graph of order n is known as an n -order graph. The problem of determining trees possessing the minimum ABS index among all n -order trees with fixed number of leaves has recently been attacked in two preprints independently. This article provides a complete solution to the maximal version of the aforementioned problem","PeriodicalId":36023,"journal":{"name":"Discrete Mathematics Letters","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43426990","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: 6
Variant Alternating Euler Sums of Higher Order 高阶变交替欧拉和
IF 0.8
Discrete Mathematics Letters Pub Date : 2023-03-08 DOI: 10.47443/dml.2022.192
A. Sofo
{"title":"Variant Alternating Euler Sums of Higher Order","authors":"A. Sofo","doi":"10.47443/dml.2022.192","DOIUrl":"https://doi.org/10.47443/dml.2022.192","url":null,"abstract":"A family of alternating variant Euler sums of higher order is investigated. A number of different examples concerning the main theorem are given. A Log-PolyLog integral in terms of special functions is also evaluated.","PeriodicalId":36023,"journal":{"name":"Discrete Mathematics Letters","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44403231","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
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