Results 21 to 30 of about 128 (115)
Minimizing cycles in tournaments and normalized \(q\)-norms [PDF]
, 2022 Akin to the Erdős-Rademacher problem, Linial and Morgenstern made the following conjecture in tournaments: for any \(d\in (0,1]\), among all \(n\)-vertex tournaments with \(d\binom{n}{3}\) many 3-cycles, the number of 4-cycles is asymptotically minimized
Tang, Tianyun, Ma, Jie
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Discussiones Mathematicae Graph Theory, 2022 We introduce a new notion of circular colourings for digraphs. The idea of this quantity, called star dichromatic number χ→*\vec \chi * (D) of a digraph D, is to allow a finer subdivision of digraphs with the same dichromatic number into such which are ...
Hochstättler Winfried, Steiner Raphael
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Hamiltonian Cycle Problem in Strong k-Quasi-Transitive Digraphs With Large Diameter
Discussiones Mathematicae Graph Theory, 2021 Let k be an integer with k ≥ 2. A digraph is k-quasi-transitive, if for any path x0x1... xk of length k, x0 and xk are adjacent. Let D be a strong k-quasi-transitive digraph with even k ≥ 4 and diameter at least k +2.
Wang Ruixia
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H-Kernels in Unions of H-Colored Quasi-Transitive Digraphs
Discussiones Mathematicae Graph Theory, 2021 Let H be a digraph (possibly with loops) and D a digraph without loops whose arcs are colored with the vertices of H (D is said to be an H-colored digraph). For an arc (x, y) of D, its color is denoted by c(x, y). A directed path W = (v0, . .
Campero-Alonzo José Manuel +1 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
On sunlet graphs connected to a specific map on {1, 2, . . . , p − 1} [PDF]
, 2018 In this article, we study the structure of the graph implied by a given map on the set Sp = {1, 2, . . . , p − 1}, where p is an odd prime. The consecutive applications of the map generate an integer sequence, or in graph theoretical context a walk ...
Németh, László +2 more
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The Second Neighbourhood for Bipartite Tournaments
Discussiones Mathematicae Graph Theory, 2019 Let T (X ∪ Y, A) be a bipartite tournament with partite sets X, Y and arc set A. For any vertex x ∈ X ∪Y, the second out-neighbourhood N++(x) of x is the set of all vertices with distance 2 from x.
Li Ruijuan, Sheng Bin
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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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The {−2,−1}-Selfdual and Decomposable Tournaments
Discussiones Mathematicae Graph Theory, 2018 We only consider finite tournaments. The dual of a tournament is obtained by reversing all the arcs. A tournament is selfdual if it is isomorphic to its dual.
Boudabbous Youssef, Ille Pierre
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On the n-Partite Tournaments with Exactly n − m + 1 Cycles of Length m
Discussiones Mathematicae Graph Theory, 2021 Gutin and Rafiey [Multipartite tournaments with small number of cycles, Australas J. Combin. 34 (2006) 17–21] raised the following two problems: (1) Let m ∈ {3, 4, . . ., n}.
Guo Qiaoping, Meng Wei
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