Results 11 to 20 of about 101 (95)
Largest nearest-neighbour link and connectivity threshold in a polytopal random sample [PDF]
, 2023 A preprint version of the article is available at arXiv:2301.02506v1 [math.PR], https://arxiv.org/abs/2301.02506.. It has not been certified by peer-review.A CC BY or equivalent licence is applied to the AAM arising from this submission, in accordance ...
Penrose, MD, Higgs, F, Yang, X
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More on the Rainbow Disconnection in Graphs
Discussiones Mathematicae Graph Theory, 2022 Let G be a nontrivial edge-colored connected graph. An edge-cut R of G is called a rainbow-cut if no two of its edges are colored the same. An edge-colored graph G is rainbow disconnected if for every two vertices u and v of G, there exists a u-v-rainbow-
Bai Xuqing +3 more
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Some results on the total proper k-connection number
Open Mathematics, 2022 In this paper, we first investigate the total proper connection number of a graph GG according to some constraints of G¯\overline{G}. Next, we investigate the total proper connection numbers of graph GG with large clique number ω(G)=n−s\omega \left(G)=n ...
Ma Yingbin, Zhang Hui
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Generalized 4-connectivity of hierarchical star networks
Open Mathematics, 2022 The connectivity is an important measurement for the fault-tolerance of a network. The generalized connectivity is a natural generalization of the classical connectivity. An SS-tree of a connected graph GG is a tree T=(V′,E′)T=\left(V^{\prime} ,E^{\prime}
Wang Junzhen, Zou Jinyu, Zhang Shumin
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The structure fault tolerance of burnt pancake networks
Open Mathematics, 2023 One of the symbolic parameters to measure the fault tolerance of a network is its connectivity. The HH-structure connectivity and HH-substructure connectivity extend the classical connectivity and are more practical.
Ge Huifen, Ye Chengfu, Zhang Shumin
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Large Contractible Subgraphs of a 3-Connected Graph
Discussiones Mathematicae Graph Theory, 2021 Let m ≥ 5 be a positive integer and let G be a 3-connected graph on at least 2m + 1 vertices. We prove that G has a contractible set W such that m ≤ W ≤ 2m − 4.
Karpov Dmitri V.
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Conflict-Free Vertex-Connections of Graphs
Discussiones Mathematicae Graph Theory, 2020 A path in a vertex-colored graph is called conflict-free if there is a color used on exactly one of its vertices. A vertex-colored graph is said to be conflict-free vertex-connected if any two vertices of the graph are connected by a conflict-free path ...
Li Xueliang +5 more
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The Minimum Size of a Graph with Given Tree Connectivity
Discussiones Mathematicae Graph Theory, 2021 For a graph G = (V, E) and a set S ⊆ V of at least two vertices, an S-tree is a such subgraph T of G that is a tree with S ⊆ V (T). Two S-trees T1 and T2 are said to be internally disjoint if E(T1) ∩ E(T2) = ∅ and V (T1) ∩ V (T2) = S, and edge-disjoint ...
Sun Yuefang, Sheng Bin, Jin Zemin
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The Vertex-Rainbow Connection Number of Some Graph Operations
Discussiones Mathematicae Graph Theory, 2021 A path in an edge-colored (respectively vertex-colored) graph G is rainbow (respectively vertex-rainbow) if no two edges (respectively internal vertices) of the path are colored the same.
Li Hengzhe, Ma Yingbin, Li Xueliang
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Discussiones Mathematicae Graph Theory, 2021 Let G be a 4-connected graph G, and let Ec(G) denote the set of 4-contractible edges of G. We prove results concerning the distribution of edges in Ec(G). Roughly speaking, we show that there exists a set K0 and a mapping φ : K0 → Ec(G) such that |φ −1(e)
Nakamura Shunsuke
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