Graphs and Combinatorics最新文献_第9页

Fixing Numbers of Graphs with Symmetric and Generalized Quaternion Symmetry Groups 对称和广义四元对称群图形的固定数

IF 0.7 4区数学

Graphs and Combinatorics Pub Date : 2024-01-19 DOI: 10.1007/s00373-023-02742-9

Christina Graves, L.-K. Lauderdale

引用次数: 0

A Construction of Optimal 1-Spontaneous Emission Error Designs 最佳 1 自发发射误差设计的构建

IF 0.7 4区数学

Graphs and Combinatorics Pub Date : 2024-01-19 DOI: 10.1007/s00373-023-02743-8

Junling Zhou, Na Zhang

{"title":"A Construction of Optimal 1-Spontaneous Emission Error Designs","authors":"Junling Zhou, Na Zhang","doi":"10.1007/s00373-023-02743-8","DOIUrl":"https://doi.org/10.1007/s00373-023-02743-8","url":null,"abstract":"A t-spontaneous emission error design, denoted by t-(v, k; m) SEED or t-SEED in short, is a system ({{mathcal {B}}}) of k-subsets of a v-set V with a partition ({{mathcal {B}}}_1,mathcal{B}_2,ldots ,{{mathcal {B}}}_{m}) of ({{mathcal {B}}}) satisfying ({{|{Bin {mathcal {B}}_i:, E subseteq B}|}over {|{mathcal {B}}_i|}}=mu _E ) for any (1le ile m) and (Esubseteq V), (|E|le t), where (mu _E) is a constant depending only on E. A t-(v, k; m) SEED is an important combinatorial object with applications in quantum jump codes. The number m is called the dimension of the t-SEED and this corresponds to the number of orthogonal basis states in a quantum jump code. For given v, k and t, a t-(v, k; m) SEED is called optimal when m achieves the largest possible dimension. When (kmid v), an optimal 1-(v, k; m) SEED has dimension ({v-1atopwithdelims ()k-1}) and can be constructed by Baranyai’s Theorem. This note investigates optimal 1-(v, k; m) SEEDs with (knot mid v), in which a generalization of Baranyai’s Theorem plays a significant role. To be specific, we construct an optimal 1-(v, k; m) SEED for all positive integers v, k, s with (vequiv -s) (mod k), (kge s+1) and (vge max {2k, s(2k-1)}).\u0000","PeriodicalId":12811,"journal":{"name":"Graphs and Combinatorics","volume":"41 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139498278","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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

Equality of Ordinary and Symbolic Powers of Some Classes of Monomial Ideals 某些类单项式理想的普通幂和符号幂的等价性

IF 0.7 4区数学

Graphs and Combinatorics Pub Date : 2024-01-19 DOI: 10.1007/s00373-023-02740-x

Kanoy Kumar Das

引用次数: 0

Compatible Spanning Circuits and Forbidden Induced Subgraphs 兼容跨电路和禁止诱导子图

IF 0.7 4区数学

Graphs and Combinatorics Pub Date : 2024-01-19 DOI: 10.1007/s00373-023-02735-8

Zhiwei Guo, Christoph Brause, Maximilian Geißer, Ingo Schiermeyer

{"title":"Compatible Spanning Circuits and Forbidden Induced Subgraphs","authors":"Zhiwei Guo, Christoph Brause, Maximilian Geißer, Ingo Schiermeyer","doi":"10.1007/s00373-023-02735-8","DOIUrl":"https://doi.org/10.1007/s00373-023-02735-8","url":null,"abstract":"A compatible spanning circuit in an edge-colored graph G (not necessarily properly) is defined as a closed trail containing all vertices of G in which any two consecutively traversed edges have distinct colors. The existence of extremal compatible spanning circuits (i.e., compatible Hamilton cycles and compatible Euler tours) has been studied extensively. Recently, sufficient conditions for the existence of compatible spanning circuits visiting each vertex at least a specified number of times in specific edge-colored graphs satisfying certain degree conditions have been established. In this paper, we continue the research on sufficient conditions for the existence of such compatible s-panning circuits. We consider edge-colored graphs containing no certain forbidden induced subgraphs. As applications, we also consider the existence of such compatible spanning circuits in edge-colored graphs G with κ(G) ≥ α(G), κ(G) ≥ α(G) − 1 and κ (G) ≥ α(G), respectively. In this context, κ(G), α(G) and κ (G) denote the connectivity, the independence number and the edge connectivity of a graph G, respectively.","PeriodicalId":12811,"journal":{"name":"Graphs and Combinatorics","volume":"5 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139498279","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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

Path Planning in a Weighted Planar Subdivision Under the Manhattan Metric 曼哈顿度量下的加权平面细分中的路径规划

IF 0.7 4区数学

Graphs and Combinatorics Pub Date : 2024-01-19 DOI: 10.1007/s00373-023-02744-7

Mansoor Davoodi, Ashkan Safari

引用次数: 0

Coloring of Graphs Avoiding Bicolored Paths of a Fixed Length 避免固定长度双色路径的图形着色

IF 0.7 4区数学

Graphs and Combinatorics Pub Date : 2024-01-11 DOI: 10.1007/s00373-023-02739-4

Alaittin Kırtışoğlu, Lale Özkahya

{"title":"Coloring of Graphs Avoiding Bicolored Paths of a Fixed Length","authors":"Alaittin Kırtışoğlu, Lale Özkahya","doi":"10.1007/s00373-023-02739-4","DOIUrl":"https://doi.org/10.1007/s00373-023-02739-4","url":null,"abstract":"The problem of finding the minimum number of colors to color a graph properly without containing any bicolored copy of a fixed family of subgraphs has been widely studied. Most well-known examples are star coloring and acyclic coloring of graphs (Grünbaum in Isreal J Math 14(4):390–498, 1973) where bicolored copies of (P_4) and cycles are not allowed, respectively. In this paper, we introduce a variation of these problems and study proper coloring of graphs not containing a bicolored path of a fixed length and provide general bounds for all graphs. A (P_k)-coloring of an undirected graph G is a proper vertex coloring of G such that there is no bicolored copy of (P_k) in G, and the minimum number of colors needed for a (P_k)-coloring of G is called the (P_k)-chromatic number of G, denoted by (s_k(G).) We provide bounds on (s_k(G)) for all graphs, in particular, proving that for any graph G with maximum degree (dge 2,) and (kge 4,) (s_k(G)le lceil 6sqrt{10}d^{frac{k-1}{k-2}} rceil .) Moreover, we find the exact values for the (P_k)-chromatic number of the products of some cycles and paths for (k=5,6.)","PeriodicalId":12811,"journal":{"name":"Graphs and Combinatorics","volume":"3 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139465047","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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

Note on Polychromatic Coloring of Hereditary Hypergraph Families. 遗传超图族的多色着色注释。

IF 0.6 4区数学

Graphs and Combinatorics Pub Date : 2024-01-01 Epub Date: 2024-11-22 DOI: 10.1007/s00373-024-02836-y

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