Results 31 to 40 of about 635 (107)
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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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
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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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
wiley +1 more source
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
wiley +1 more source
On the stability for pancyclicity
Discussiones Mathematicae Graph Theory, 2001 Summary: A property \(P\) defined on all graphs of order \(n\) is said to be \(k\)-stable if for any graph of order \(n\) that does not satisfy \(P\), the fact that \(uv\) is not an edge of \(G\) and that \(G+ uv\) satisfies \(P\) implies \(d_G(u)+ d_G(v)< k\). Every property is \((2n-3)\)-stable and every \(k\)-stable property is \((k+1)\)-stable.
openaire +2 more sources
Note on Hamiltonicity of Basis Graphs of Even Delta‐Matroids
Journal of Graph Theory, Volume 109, Issue 4, Page 446-453, August 2025.ABSTRACT We show that the basis graph of an even delta‐matroid is Hamiltonian if it has more than two vertices. More strongly, we prove that for two distinct edges e and f sharing a common end, it has a Hamiltonian cycle using e and avoiding f unless it has at most two vertices or it is a cycle of length at most four.
Donggyu Kim, Sang‐il Oum
wiley +1 more source
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
Two-Disjoint-Cycle-Cover Pancyclicity of Dragonfly Networks
MathematicsInterconnection networks (often modeled as graphs) are critical for high-performance computing systems, as they have significant impact on performance metrics like latency and bandwidth.
Zengxian Tian, Guanlin He
doaj +1 more source
On pancyclic arcs in hypertournaments
Discrete Applied Mathematics, 2016 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hongwei Li 0018 +3 more
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