Results 31 to 40 of about 89 (84)
On the Maximum and Minimum Sizes of a Graph with Given k-Connectivity
Discussiones Mathematicae Graph Theory, 2017 The concept of k-connectivity κk(G), introduced by Chartrand in 1984, is a generalization of the cut-version of the classical connectivity. For an integer k ≥ 2, the k-connectivity of a connected graph G with order n ≥ k is the smallest number of ...
Sun Yuefang
doaj +1 more source
More Aspects of Arbitrarily Partitionable Graphs
Discussiones Mathematicae Graph Theory, 2022 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.
Bensmail Julien, Li Binlong
doaj +1 more source
Minimally Strong Subgraph (k,ℓ)-Arc-Connected Digraphs
Discussiones Mathematicae Graph Theory, 2022 Let D = (V,A) be a digraph of order n, S a subset of V of size k and 2 ≤ k ≤ n. A subdigraph H of D is called an S-strong subgraph if H is strong and S ⊆ V (H). Two S-strong subgraphs D1 and D2 are said to be arc-disjoint if A(D1) ∩ A(D2) = ∅.
Sun Yuefang, Jin Zemin
doaj +1 more source
Removable Edges on a Hamilton Cycle or Outside a Cycle in a 4-Connected Graph
Discussiones Mathematicae Graph Theory, 2021 Let G be a 4-connected graph. We call an edge e of G removable if the following sequence of operations results in a 4-connected graph: delete e from G; if there are vertices with degree 3 in G− e, then for each (of the at most two) such vertex x, delete ...
Wu Jichang +3 more
doaj +1 more source
Deficiency and Forbidden Subgraphs of Connected, Locally-Connected Graphs
Discussiones Mathematicae Graph Theory, 2020 A graph G is locally-connected if the neighbourhood NG(v) induces a connected subgraph for each vertex v in G. For a graph G, the deficiency of G is the number of vertices unsaturated by a maximum matching, denoted by def(G). In fact, the deficiency of a
Li Xihe, Wang Ligong
doaj +1 more source
The super-connectivity of Johnson graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 For positive integers $n,k$ and $t$, the uniform subset graph $G(n, k, t)$ has all $k$-subsets of $\{1,2,\ldots, n\}$ as vertices and two $k$-subsets are joined by an edge if they intersect at exactly $t$ elements.
Gülnaz Boruzanlı Ekinci +1 more
doaj +1 more source
Rainbow Disconnection in Graphs
Discussiones Mathematicae Graph Theory, 2018 Let G be a nontrivial connected, edge-colored graph. An edge-cut R of G is called a rainbow cut if no two edges in R are colored the same. An edge-coloring of G is a rainbow disconnection coloring if for every two distinct vertices u and v of G, there ...
Chartrand Gary +4 more
doaj +1 more source
Picture Fuzzy Incidence Graphs with Application
, 2021 In this research article, we initiate the novel idea of picturefuzzy incidence graphs (PFIGs). We explain some innovative notionscomprising of picture fuzzy cut-vertices, picture fuzzy bridges, picturefuzzy incidence cutpairs, and picture fuzzy incidence
Irfan Nazeer; Department of Mathematics, University of management and technology, Lahore 54770 +1 more
core
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
doaj +1 more source
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
core +1 more source