Results 41 to 50 of about 101 (95)
On the Optimality of 3-Restricted Arc Connectivity for Digraphs and Bipartite Digraphs
Discussiones Mathematicae Graph Theory, 2022 Let D be a strong digraph. An arc subset S is a k-restricted arc cut of D if D − S has a strong component D′ with order at least k such that D\V (D′) contains a connected subdigraph with order at least k.
Zhang Yaoyao, Meng Jixiang
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Refining trees of tangles in abstract separation systems: inessential parts [PDF]
Robertson and Seymour proved two fundamental theorems about tangles in graphs: the tree-of-tangles theorem, which says that every graph has a tree-decomposition such that distinguishable tangles live in different nodes of the tree, and the tangle-tree ...
Albrechtsen, Sandra
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On Two Generalized Connectivities of Graphs
Discussiones Mathematicae Graph Theory, 2018 The concept of generalized k-connectivity κk(G), mentioned by Hager in 1985, is a natural generalization of the path-version of the classical connectivity.
Sun Yuefang, Li Fengwei, Jin Zemin
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Generalized Rainbow Connection of Graphs and their Complements
Discussiones Mathematicae Graph Theory, 2018 Let G be an edge-colored connected graph. A path P in G is called ℓ-rainbow if each subpath of length at most ℓ + 1 is rainbow. The graph G is called (k, ℓ)-rainbow connected if there is an edge-coloring such that every pair of distinct vertices of G is ...
Li Xueliang +3 more
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Highly connected orientations from edge-disjoint rigid subgraphs
Forum of Mathematics, PiWe give an affirmative answer to a long-standing conjecture of Thomassen, stating that every sufficiently highly connected graph has a k-vertex-connected orientation. We prove that a connectivity of order $O(k^2)$ suffices.
Dániel Garamvölgyi +3 more
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The Super-Connectivity of Kneser Graphs
Discussiones Mathematicae Graph Theory, 2019 A vertex cut of a connected graph G is a set of vertices whose deletion disconnects G. A connected graph G is super-connected if the deletion of every minimum vertex cut of G isolates a vertex.
Ekinci Gülnaz Boruzanli +1 more
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On Conditional Connectivity of the Cartesian Product of Cycles
Discussiones Mathematicae Graph Theory, 2023 The conditional h-vertex (h-edge) connectivity of a connected graph H of minimum degree k > h is the size of a smallest vertex (edge) set F of H such that H − F is a disconnected graph of minimum degree at least h. Let G be the Cartesian product of r ≥ 1
Saraf J.B., Borse Y.M., Mundhe Ganesh
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Characterizing Atoms that Result from Decomposition by Clique Separators
Discussiones Mathematicae Graph Theory, 2017 A graph is defined to be an atom if no minimal vertex separator induces a complete subgraph; thus, atoms are the graphs that are immune to clique separator decomposition.
McKee Terry A.
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The generalized 3-connectivity of burnt pancake graphs and godan graphs
AKCE International Journal of Graphs and Combinatorics, 2023 The generalized k-connectivity of a graph G, denoted by [Formula: see text] is the minimum number of internally edge disjoint S-trees for any [Formula: see text] and [Formula: see text] The generalized k-connectivity is a natural extension of the ...
Jing Wang, Zuozheng Zhang, Yuanqiu Huang
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The Double Roman Domatic Number of a Digraph
Discussiones Mathematicae Graph Theory, 2020 A double Roman dominating function on a digraph D with vertex set V (D) is defined in [G. Hao, X. Chen and L. Volkmann, Double Roman domination in digraphs, Bull. Malays. Math. Sci. Soc. (2017).] as a function f : V (D) → {0, 1, 2, 3} having the property
Volkmann Lutz
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