Results 11 to 20 of about 97 (92)
A canonical tree-of-tangles theorem for structurally submodular separation systems [PDF]
, 2021 We show that every structurally submodular separation system admits a canonical tree set which distinguishes its tangles.Mathematics Subject Classifications: 05C40, 05C83 ...
Elbracht, Christian, Kneip, Jakob
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On the Essential Element Graph of a Lattice [PDF]
, 2022 ▪ 2010 AMS Classification: 13A70, 05C40, 06A07.Let mathcalL be a bounded lattice. The essential element graph of mathcalL is a simple undirected graph varepsilonmathcalL such that the elements x,y of mathcalL form an edge in varepsilonmathcalL, whenever ...
ÜLKER, ALPER, Alper ÜLKER
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Friends and strangers walking on graphs [PDF]
, 2021 Given graphs \(X\) and \(Y\) with vertex sets \(V(X)\) and \(V(Y)\) of the same cardinality, we define a graph \(\mathsf{FS}(X,Y)\) whose vertex set consists of all bijections \(\sigma\colon V(X)\to V(Y)\), where two bijections \(\sigma\) and \(\sigma'\)
Kravitz, Noah, Defant, Colin
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The Strong 3-Rainbow Index of Graphs Containing Three Cycles [PDF]
, 2023 The concept of a strong k-rainbow index is a generalization of a strong rainbow connection number, which has an interesting application in security systems in a communication network.
Zata Yumni Awanis
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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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Some Remarks on λp,q-Connectedness [PDF]
, 2007 A connected graph is λp,q-connected if there is a set of edges whose deletion leaves two components of order at least p and q, respectively. In this paper we present some sufficient conditions for graphs to be λp,q-connected.
Rautenbach, Dieter +3 more
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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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Cyclic sums, network sharing, and restricted edge cuts in graphs with long cycles [PDF]
, 2007 Cyclic Sums, Network Sharing and Restricted Edge Cuts in Graphs with Long Cycles Dieter Rautenbach , Lutz Volkmann Preprint series: 07-06, 8 MSC 2000 05A17 Partitions of integers 05C40 Connectivity Abstract We study graphs G = (V,E ...
Rautenbach, Dieter, Volkmann, Lutz
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