Results 61 to 70 of about 1,777 (160)
Old and new generalizations of line graphs
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 29, Page 1509-1521, 2004., 2004 Line graphs have been studied for over seventy years. In 1932, H. Whitney showed that for connected graphs, edge‐isomorphism implies isomorphism except for K3 and K1,3. The line graph transformation is one of the most widely studied of all graph transformations.
Jay Bagga
wiley +1 more source
Pancyclic orderings of in-tournaments
Discrete Applied Mathematics, 1999 AbstractAn in-tournament is an oriented graph such that the negative neighborhood of every vertex induces a tournament. In this paper, pancyclic orderings of a strong in-tournament D are investigated. This is a labeling, say x1,x2,…,xn, of the vertex set of D such that D[{x1,x2,…,xt}] is Hamiltonian for t=3,4,…,n.
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Pancyclism in hamiltonian graphs
Discrete Mathematics, 1991 AbstractWe prove the following theorem. If G is a hamiltonian, nonbipartite graph of minimum degree at least (2n+1)5, where n represents the order of G, then G is pancyclic.
Denise Amar +3 more
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Cycles and matchings in randomly perturbed digraphs and hypergraphs
, 2016 We give several results showing that different discrete structures typically gain certain spanning substructures (in particular, Hamilton cycles) after a modest random perturbation.
Krivelevich, Michael +2 more
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Long cycles in certain graphs of large degree
International Journal of Mathematics and Mathematical Sciences, Volume 24, Issue 10, Page 691-697, 2000., 2000 Let G be a connected graph of order n and X = {x ∈ V : d(x) ≥ n/2}. Suppose |X| ≥ 3 and G satisfies the modified Fan′s condition. We show that the vertices of the block B of G containing X form a cycle. This generalizes a result of Fan. We also give an efficient algorithm to obtain such a cycle. The complexity of this algorithm is O(n2). In case G is 2‐
Pak-Ken Wong
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Locally Pancyclic Graphs [PDF]
Journal of Combinatorial Theory, Series B, 1999 AbstractWe prove the following theorem. LetGbe a graph of ordernand letW⊆V(G). If |W|⩾3 anddG(x)+dG(y)⩾nfor every pair of non-adjacent verticesx, y∈W, then eitherGcontains cyclesC3, C4, …, C|W|such thatCicontains exactlyivertices fromW(i=3, 4, …, |W|), or |W|=nandG=Kn/2, n/2, or else |W|=4,G[W]=K2, 2. This generalizes a result of J. A.
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Notes on a conjecture of Manoussakis concerning Hamilton cycles in digraphs
, 2014 In 1992, Manoussakis conjectured that a strongly 2-connected digraph $D$ on $n$ vertices is hamiltonian if for every two distinct pairs of independent vertices $x,y$ and $w,z$ we have $d(x)+d(y)+d(w)+d(z)\geq 4n-3$.
Ning, Bo
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Graphs with at most two moplexes
Journal of Graph Theory, Volume 107, Issue 1, Page 38-69, September 2024.Abstract A moplex is a natural graph structure that arises when lifting Dirac's classical theorem from chordal graphs to general graphs. The notion is known to be closely related to lexicographic searches in graphs as well as to asteroidal triples, and has been applied in several algorithms related to graph classes, such as interval graphs, claw‐free ...
Clément Dallard +4 more
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A Note on Long non-Hamiltonian Cycles in One Class of Digraphs
, 2012 Let $D$ be a strong digraph on $n\geq 4$ vertices. In [3, Discrete Applied Math., 95 (1999) 77-87)], J. Bang-Jensen, Y. Guo and A. Yeo proved the following theorem: if (*) $d(x)+d(y)\geq 2n-1$ and $min \{d^+(x)+ d^-(y),d^-(x)+ d^+(y)\}\geq n-1$ for every
Darbinyan, S. Kh., Karapetyan, I. A.
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Long cycles and paths in distance graphs [PDF]
, 2009 For n∈N and D⊆N, the distance graph PnD has vertex set {0,1,…,n−1} and edge set {ij∣0≤i,j≤n−1,|j−i|∈D}. Note that the important and very well-studied circulant graphs coincide with the regular distance graphs.A fundamental result concerning circulant ...
Penso, Lucia Draque +2 more
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