Results 51 to 60 of about 1,031 (124)
Another cycle structure theorem for hamiltonian graphs [PDF]
, 1999 A graph G is pancyclic if it contains a k-cycle for k = 3,4,…,|V(G)|. In this paper we show a cycle theorem as follows: If C is a hamiltonian cycle of a graph G of order n, where two non-adjacent vertices x,y at distance 2 on C satisfy d(x)+d(y) ⩾ n ...
Han, Ren
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A Fan-Type Heavy Pair Of Subgraphs For Pancyclicity Of 2-Connected Graphs
Discussiones Mathematicae Graph Theory, 2016 Let G be a graph on n vertices and let H be a given graph. We say that G is pancyclic, if it contains cycles of all lengths from 3 up to n, and that it is H-f1-heavy, if for every induced subgraph K of G isomorphic to H and every two vertices u, v ∈ V (K)
Wideł Wojciech
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A sufficient condition for pancyclability of graphs
Discrete Mathematics, 2009 AbstractLet G be a graph of order n and S be a vertex set of q vertices. We call G,S-pancyclable, if for every integer i with 3≤i≤q there exists a cycle C in G such that |V(C)∩S|=i. For any two nonadjacent vertices u,v of S, we say that u,v are of distance two in S, denoted by dS(u,v)=2, if there is a path P in G connecting u and v such that |V(P)∩S|≤3.
Hao Li, Bing Wei, Evelyne Flandrin
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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
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Tight Hamilton Cycles in Random Uniform Hypergraphs [PDF]
, 2010 In this paper we show that $e/n$ is the sharp threshold for the existence of tight Hamilton cycles in random $k$-uniform hypergraphs, for all $k\ge 4$. When $k=3$ we show that $1/n$ is an asymptotic threshold.
Dudek, Andrzej, Frieze, Alan
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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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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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A Triple of Heavy Subgraphs Ensuring Pancyclicity of 2-Connected Graphs
Discussiones Mathematicae Graph Theory, 2017 A graph G on n vertices is said to be pancyclic if it contains cycles of all lengths k for k ∈ {3, . . . , n}. A vertex v ∈ V (G) is called super-heavy if the number of its neighbours in G is at least (n+1)/2.
Wide Wojciech
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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
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A sufficient condition for pre-Hamiltonian cycles in bipartite digraphs
, 2017 Let $D$ be a strongly connected balanced bipartite directed graph of order $2a\geq 10$ other than a directed cycle. Let $x,y$ be distinct vertices in $D$.
Darbinyan, Samvel Kh. +1 more
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