Results 11 to 20 of about 778 (78)
Strong Geodetic Problem in Networks
Discussiones Mathematicae Graph Theory, 2020 In order to model certain social network problems, the strong geodetic problem and its related invariant, the strong geodetic number, are introduced.
Manuel Paul +4 more
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Decomposing tournaments into paths
Proceedings of the London Mathematical Society, Volume 121, Issue 2, Page 426-461, August 2020., 2020 Abstract We consider a generalisation of Kelly's conjecture which is due to Alspach, Mason, and Pullman from 1976. Kelly's conjecture states that every regular tournament has an edge decomposition into Hamilton cycles, and this was proved by Kühn and Osthus for large tournaments. The conjecture of Alspach, Mason, and Pullman asks for the minimum number
Allan Lo +3 more
wiley +1 more source
Discussiones Mathematicae Graph Theory, 2020 If S = (a1, a2, . . .) is a non-decreasing sequence of positive integers, then an S-packing coloring of a graph G is a partition of V (G) into sets X1, X2, . . .
Brešar Boštjan +3 more
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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
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On the Number of Disjoint 4-Cycles in Regular Tournaments
Discussiones Mathematicae Graph Theory, 2018 In this paper, we prove that for an integer r ≥ 1, every regular tournament T of degree 3r − 1 contains at least 2116r-103${{21} \over {16}}r - {{10} \over 3}$ disjoint directed 4-cycles. Our result is an improvement of Lichiardopol’s theorem when taking
Ma Fuhong, Yan Jin
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Graphs that are Critical for the Packing Chromatic Number
Discussiones Mathematicae Graph Theory, 2022 Given a graph G, a coloring c : V (G) → {1, …, k} such that c(u) = c(v) = i implies that vertices u and v are at distance greater than i, is called a packing coloring of G.
Brešar Boštjan, Ferme Jasmina
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The Existence of Path-Factor Covered Graphs
Discussiones Mathematicae Graph Theory, 2023 A spanning subgraph H of a graph G is called a P≥k-factor of G if every component of H is isomorphic to a path of order at least k, where k ≥ 2. A graph G is called a P≥k-factor covered graph if there is a P≥k-factor of G covering e for any e ∈ E(G).
Dai Guowei
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Equimatchable Bipartite Graphs
Discussiones Mathematicae Graph Theory, 2023 A graph is called equimatchable if all of its maximal matchings have the same size. Lesk et al. [Equi-matchable graphs, Graph Theory and Combinatorics (Academic Press, London, 1984) 239–254] has provided a characterization of equimatchable bipartite ...
Büyükçolak Yasemin +2 more
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An asymptotic bound for the strong chromatic number [PDF]
, 2018 The strong chromatic number $\chi_{\text{s}}(G)$ of a graph $G$ on $n$ vertices is the least number $r$ with the following property: after adding $r \lceil n/r \rceil - n$ isolated vertices to $G$ and taking the union with any collection of spanning ...
Lo, Allan, Sanhueza-Matamala, Nicolás
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Turán Function and H-Decomposition Problem for Gem Graphs
Discussiones Mathematicae Graph Theory, 2018 Given a graph H, the Turán function ex(n,H) is the maximum number of edges in a graph on n vertices not containing H as a subgraph. For two graphs G and H, an H-decomposition of G is a partition of the edge set of G such that each part is either a single
Liu Henry, Sousa Teresa
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