Discussiones Mathematicae Graph Theory最新文献_第9页

Distance-Local Rainbow Connection Number 距离-本地彩虹连接号

IF 0.7 4区数学

Discussiones Mathematicae Graph Theory Pub Date : 2022-07-12 DOI: 10.7151/dmgt.2325

F. Septyanto, K. Sugeng

引用次数: 2

Nested Locally Hamiltonian Graphs and the Oberly-Sumner Conjecture 嵌套局部Hamilton图与Oberly-Sumner猜想

IF 0.7 4区数学

Discussiones Mathematicae Graph Theory Pub Date : 2022-07-12 DOI: 10.7151/dmgt.2346

Johan P. de Wet, M. Frick

{"title":"Nested Locally Hamiltonian Graphs and the Oberly-Sumner Conjecture","authors":"Johan P. de Wet, M. Frick","doi":"10.7151/dmgt.2346","DOIUrl":"https://doi.org/10.7151/dmgt.2346","url":null,"abstract":"Abstract A graph G is locally 𝒫, abbreviated L𝒫, if for every vertex v in G the open neighbourhood N(v) of v is non-empty and induces a graph with property 𝒫. Specifically, a graph G without isolated vertices is locally connected (LC) if N(v) induces a connected graph for each v ∈ V (G), and locally hamiltonian (LH) if N(v) induces a hamiltonian graph for each v ∈ V (G). A graph G is locally locally 𝒫 (abbreviated L2𝒫) if N(v) is non-empty and induces a locally 𝒫 graph for every v ∈ V (G). This concept is generalized to an arbitrary degree of nesting. For any k 0 we call a graph locally k-nested-hamiltonian if it is LmC for m = 0, 1, . . ., k and LkH (with L0C and L0H meaning connected and hamiltonian, respectively). The class of locally k-nested-hamiltonian graphs contains important subclasses. For example, Skupień had already observed in 1963 that the class of connected LH graphs (which is the class of locally 1-nested-hamiltonian graphs) contains all triangulations of closed surfaces. We show that for any k ≥ 1 the class of locally k-nested-hamiltonian graphs contains all simple-clique (k + 2)-trees. In 1979 Oberly and Sumner proved that every connected K1,3-free graph that is locally connected is hamiltonian. They conjectured that for k ≥ 1, every connected K1,k+3-free graph that is locally (k + 1)-connected is hamiltonian. We show that locally k-nested-hamiltonian graphs are locally (k + 1)-connected and consider the weaker conjecture that every K1,k+3-free graph that is locally k-nested-hamiltonian is hamiltonian. We show that if our conjecture is true, it would be “best possible” in the sense that for every k ≥ 1 there exist K1,k+4-free locally k-nested-hamiltonian graphs that are non-hamiltonian. We also attempt to determine the minimum order of non-hamiltonian locally k-nested-hamiltonian graphs and investigate the complexity of the Hamilton Cycle Problem for locally k-nested-hamiltonian graphs with restricted maximum degree.","PeriodicalId":48875,"journal":{"name":"Discussiones Mathematicae Graph Theory","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42881551","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

More on Signed Graphs with at Most Three Eigenvalues 更多关于最多三个特征值的签名图

IF 0.7 4区数学

Discussiones Mathematicae Graph Theory Pub Date : 2022-07-12 DOI: 10.7151/dmgt.2393

F. Ramezani, P. Rowlinson, Z. Stanić

引用次数: 6

Flippable Edges in Triangulations on Surfaces 曲面上三角形的可翻转边

IF 0.7 4区数学

Discussiones Mathematicae Graph Theory Pub Date : 2022-07-12 DOI: 10.7151/dmgt.2377

Daiki Ikegami, Atsuhiro Nakamoto

引用次数: 0

On Mf-Edge Colorings of Graphs 关于图的mf边着色

IF 0.7 4区数学

Discussiones Mathematicae Graph Theory Pub Date : 2022-07-12 DOI: 10.7151/dmgt.2329

J. Ivanco, Alfréd Onderko

引用次数: 1

Bounds on the Double Italian Domination Number of a Graph 图的双意大利支配数的界

IF 0.7 4区数学

Discussiones Mathematicae Graph Theory Pub Date : 2022-07-12 DOI: 10.7151/dmgt.2330

Farzaneh Azvin, N. J. Rad

引用次数: 3

More Aspects of Arbitrarily Partitionable Graphs 任意可分图的更多方面

IF 0.7 4区数学

Discussiones Mathematicae Graph Theory Pub Date : 2022-07-12 DOI: 10.7151/DMGT.2343

Julien Bensmail, Binlong Li

{"title":"More Aspects of Arbitrarily Partitionable Graphs","authors":"Julien Bensmail, Binlong Li","doi":"10.7151/DMGT.2343","DOIUrl":"https://doi.org/10.7151/DMGT.2343","url":null,"abstract":"Abstract A graph G of order n is arbitrarily partitionable (AP) if, for every sequence (n1, . . ., np) partitioning n, there is a partition (V1, . . ., ,Vp) of V (G) such that G[Vi] is a connected ni-graph for i = 1, . . ., p. The property of being AP is related to other well-known graph notions, such as perfect matchings and Hamiltonian cycles, with which it shares several properties. This work is dedicated to studying two aspects behind AP graphs. On the one hand, we consider algorithmic aspects of AP graphs, which received some attention in previous works. We first establish the NP-hardness of the problem of partitioning a graph into connected subgraphs following a given sequence, for various new graph classes of interest. We then prove that the problem of deciding whether a graph is AP is in NP for several classes of graphs, confirming a conjecture of Barth and Fournier for these. On the other hand, we consider the weakening to APness of su cient conditions for Hamiltonicity. While previous works have suggested that such conditions can sometimes indeed be weakened, we here point out cases where this is not true. This is done by considering conditions for Hamiltonicity involving squares of graphs, and claw- and net-free graphs.","PeriodicalId":48875,"journal":{"name":"Discussiones Mathematicae Graph Theory","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49401841","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: 3

Cyclic Permutations in Determining Crossing Numbers 确定交叉数的循环置换

IF 0.7 4区数学

Discussiones Mathematicae Graph Theory Pub Date : 2022-07-12 DOI: 10.7151/dmgt.2351

Marián Klesc, M. Staš

引用次数: 8

On Singular Signed Graphs with Nullspace Spanned by a Full Vector: Signed Nut Graphs 关于零空间由全向量生成的奇异有符号图：有符号Nut图

IF 0.7 4区数学

Discussiones Mathematicae Graph Theory Pub Date : 2022-07-12 DOI: 10.7151/dmgt.2436

N. Bašić, P. Fowler, T. Pisanski, Irene Sciriha

{"title":"On Singular Signed Graphs with Nullspace Spanned by a Full Vector: Signed Nut Graphs","authors":"N. Bašić, P. Fowler, T. Pisanski, Irene Sciriha","doi":"10.7151/dmgt.2436","DOIUrl":"https://doi.org/10.7151/dmgt.2436","url":null,"abstract":"Abstract A signed graph has edge weights drawn from the set {+1, −1}, and is sign-balanced if it is equivalent to an unsigned graph under the operation of sign switching; otherwise it is sign-unbalanced. A nut graph has a one dimensional kernel of the 0-1 adjacency matrix with a corresponding eigenvector that is full. In this paper we generalise the notion of nut graphs to signed graphs. Orders for which regular nut graphs with all edge weights +1 exist have been determined recently for the degrees up to 12. By extending the definition to signed graphs, we here find all pairs (ρ, n) for which a ρ-regular nut graph (sign-balanced or sign-unbalanced) of order n exists with ρ ≤ 11. We devise a construction for signed nut graphs based on a smaller ‘seed’ graph, giving infinite series of both sign-balanced and sign-unbalanced ρ -regular nut graphs. Orders for which a regular nut graph with ρ = n − 1 exists are characterised; they are sign-unbalanced with an underlying graph Kn for which n ≡ 1 (mod 4). Orders for which a regular sign-unbalanced nut graph with ρ = n − 2 exists are also characterised; they have an underlying cocktail-party graph CP(n) with even order n ≥ 8.","PeriodicalId":48875,"journal":{"name":"Discussiones Mathematicae Graph Theory","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47418390","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: 1

Graphs with Unique Maximum Packing of Closed Neighborhoods 闭邻域具有唯一最大包装的图

IF 0.7 4区数学

Discussiones Mathematicae Graph Theory Pub Date : 2022-06-29 DOI: 10.7151/dmgt.2304

D. Bozovic, Iztok Peterin

引用次数: 3