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On hyper-Zagreb index conditions for hamiltonicity of graphs
During the last decade, several research groups have published results on sufficient conditions for the hamiltonicity of graphs by using some...
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Hamiltonicity of Randomly Perturbed Graphs
The theory of randomly perturbed graphs deals with the properties of graphs obtained as the union of a deterministic graph H and a random graph G. We...
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On sufficient conditions for Hamiltonicity of graphs, and beyond
Identifying certain conditions that ensure the Hamiltonicity of graphs is highly important and valuable due to the fact that determining whether a...
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The Hamiltonicity and Hamiltonian-connectivity of Solid Supergrid Graphs
The Hamiltonian path and cycle problems are well-known NP-complete problems. A given graph is Hamiltonian-connected if there exists a Hamiltonian...
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On Sufficient Conditions for Hamiltonicity in Dense Graphs
We study structural conditions in dense graphs that guarantee the existence of vertex-spanning substructures such as Hamilton cycles. Recall that...
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A Generalization of Implicit Ore-condition for Hamiltonicity of k-connected Graphs
In 2005, Flandrin et al. proved that if G is a k -connected graph of order n and V ( G ) = X 1 ∪ X 2 ∪ ⋯ UXfc such that d ( x ) + d ( y ) ≥ n for each pair of...
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Induced Nets and Hamiltonicity of Claw-Free Graphs
The connected graph of degree sequence 3, 3, 3, 1, 1, 1 is called a net , and the vertices of degree 1 in a net are called its endvertices. Broersma...
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Perfect Matchings and Hamiltonicity in the Cartesian Product of Cycles
If every perfect matching of a graph G extends to a Hamiltonian cycle, we shall say that G has the PMH-property—a concept first studied in the 1970s...
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A Note on Singular Edges and Hamiltonicity in Claw-Free Graphs with Locally Disconnected Vertices
An edge e of a graph G is called singular if it is not on a triangle; otherwise, e is nonsingular . A vertex is called singular if it is adjacent to a...
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Hamiltonicity Below Dirac’s Condition
Dirac’s theorem (1952) is a classical result of graph theory, stating that an n-vertex graph (...
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Finding Long Cycles in Balanced Tripartite Graphs: A First Step
We consider the problem of finding long cycles in balanced tripartite graphs. We survey the relevant literature, namely degree and edge conditions...
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Wiener Index, Hyper-Wiener Index, Harary Index and Hamiltonicity Properties of graphs
In this paper, in terms of Wiener index, hyper-Wiener index and Harary index, we first give some sufficient conditions for a nearly balance bipartite...
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The Relation Between Hamiltonian and 1-Tough Properties of the Cartesian Product Graphs
The relation between Hamiltonicity and toughness of a graph is a long standing research problem. The paper studies the Hamiltonicity of the Cartesian...
