Results 51 to 60 of about 1,777 (160)
Pancyclicity When Each Cycle Contains k Chords
Discussiones Mathematicae Graph Theory, 2019 For integers n ≥ k ≥ 2, let c(n, k) be the minimum number of chords that must be added to a cycle of length n so that the resulting graph has the property that for every l ∈ {k, k + 1, . . .
Taranchuk Vladislav
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Forbidden Pairs and (k,m)-Pancyclicity
Discussiones Mathematicae Graph Theory, 2017 A graph G on n vertices is said to be (k, m)-pancyclic if every set of k vertices in G is contained in a cycle of length r for each r ∈ {m, m+1, . . . , n}.
Crane Charles Brian
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A degree characterisation of pancyclicity
Discrete Mathematics, 1994 AbstractA graph G of order n is said to be in the class O(n − 1) if deg(u) + deg(ʋ) ⩾ n − 1 for every pair of nonadjacent vertices u, ʋ ϵ V(G). We characterise the graphs in O(n − 1) which are pancyclic.
Robert E. L. Aldred +2 more
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Proof of a conjecture of Thomassen on Hamilton cycles in highly connected tournaments
Proceedings of the London Mathematical Society, Volume 109, Issue 3, Page 733-762, September 2014., 2014 A conjecture of Thomassen from 1982 states that, for every k, there is an f(k) so that every strongly f(k)‐connected tournament contains k edge‐disjoint Hamilton cycles. A classical theorem of Camion, that every strongly connected tournament contains a Hamilton cycle, implies that f(1)=1. So far, even the existence of f(2) was open.
Daniela Kühn +3 more
wiley +1 more source
On pancyclic representable matroids
Discrete Mathematics, 2005 AbstractBondy proved that an n-vertex simple Hamiltonian graph with at least n2/4 edges has cycles of every length unless it is isomorphic to Kn/2,n/2. This paper considers finding circuits of every size in GF(q)-representable matroids with large numbers of elements.
Brian Beavers, James Oxley
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New Sufficient Conditions for Hamiltonian Paths
The Scientific World Journal, Volume 2014, Issue 1, 2014., 2014 A Hamiltonian path in a graph is a path involving all the vertices of the graph. In this paper, we revisit the famous Hamiltonian path problem and present new sufficient conditions for the existence of a Hamiltonian path in a graph.
M. Sohel Rahman +3 more
wiley +1 more source
An Efficient Hierarchy Algorithm for Community Detection in Complex Networks
Mathematical Problems in Engineering, Volume 2014, Issue 1, 2014., 2014 Community structure is one of the most fundamental and important topology characteristics of complex networks. The research on community structure has wide applications and is very important for analyzing the topology structure, understanding the functions, finding the hidden properties, and forecasting the time‐varying of the networks.
Lili Zhang +5 more
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Toughness, Forbidden Subgraphs and Pancyclicity
Graphs and Combinatorics, 2021 Motivated by several conjectures due to Nikoghosyan, in a recent article due to Li et al., the aim was to characterize all possible graphs H such that every 1-tough H-free graph is hamiltonian. The almost complete answer was given there by the conclusion
Wei Zheng, H. Broersma, Ligong Wang
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Graph Invariants and Large Cycles: A Survey
International Journal of Mathematics and Mathematical Sciences, Volume 2011, Issue 1, 2011., 2011 Graph invariants provide a powerful analytical tool for investigation of abstract substructures of graphs. This paper is devoted to large cycle substructures, namely, Hamilton, longest and dominating cycles and some generalized cycles including Hamilton and dominating cycles as special cases. In this paper, we have collected 36 pure algebraic relations
Zh. G. Nikoghosyan, Howard Bell
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