On Vertices Enforcing a Hamiltonian Cycle by Fabrici Igor, Hexel Erhard, Jendrol’ Stanislav

“…A nonempty vertex set X ⊆ V (G) of a hamiltonian graph G is called an H-force set of G if every X-cycle of G (i.e. a cycle of G containing all vertices of X) is hamiltonian. …”
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Variant Of Hamilton's Icosian Game by Jo-Hanna Ho Wai Yann

“…This thesis proposes a new way of drawing and finding solutions for Hamiltonian graphs, as well as using them in a variant of Hamilton's original Icosian game. …”
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Proof Compression and NP Versus PSPACE II: Addendum by Lew Gordeev, Edward Hermann Haeusler

“…The underlying idea (due to the second author) is to omit full minimal logic and compress only “naive” normal tree-like ND refutations of the existence of Hamiltonian cycles in given non-Hamiltonian graphs, since the Hamiltonian graph problem in NPcomplete. …”
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The H-force sets of the graphs satisfying the condition of Ore’s theorem by Zhang Xinhong, Li Ruijuan

“…Let G be a Hamiltonian graph. A nonempty vertex set X⊆V(G)X\subseteq V(G) is called a Hamiltonian cycle enforcing set (in short, an H-force set) of G if every X-cycle of G (i.e., a cycle of G containing all vertices of X) is a Hamiltonian cycle. …”
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A Note on Cycles in Locally Hamiltonian and Locally Hamilton-Connected Graphs by Tang Long, Vumar Elkin

“…Oellermann and J.P.de Wet, Global cycle properties in locally connected, locally traceable and locally Hamiltonian graphs, Discrete Appl. Math. 205 (2016) 171–179] investigated the global cycle structures in connected, locally traceable/Hamiltonian graphs. …”
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On hamiltonicity of 1-tough triangle-free graphs by Wei Zheng, Hajo Broersma, Ligong Wang

“…It is well-known that every hamiltonian graph is 1-tough, but that the reverse statement is not true in general, and even not for triangle-free graphs. …”
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Cycles in edge-coloured graphs and subgraphs of random graphs by White, M

“…</p><p>The next chapter of the thesis then shows that a hamiltonian graph with minimal degree at least (5-sqrt7)n/6 contains a 2-factor with two components.…”

Ant Colony-based Optimization algorithm to overcome the pilot contamination issue within multi-cell Massive MIMO systems by Belhabib Abdelfettah, Amadid Jamal, Khabba Asma, Zeroual Abdelouhab

“…Hence, the ACO algorithm finds for each UE its enemy UE, which leads to construct a Hamiltonian graph. This graph is exploited during the assignment of the pilot sequences to the overall UEs; specifically, the linked UEs are successively allocated with the available OPSs, which leads to address the PC problem within multi-cell mMIMO systems.…”
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Asymptotically sharpening the $s$-Hamiltonian index bound by Sulin Song, Lan Lei, Yehong Shao, Hong-Jian Lai

“…For a non-negative integer $s\le |V(G)|-3$, a graph $G$ is $s$-Hamiltonian if the removal of any $k\le s$ vertices results in a Hamiltonian graph. Given a connected simple graph $G$ that is not isomorphic to a path, a cycle, or a $K_{1,3}$, let $\delta(G)$ denote the minimum degree of $G$, let $h_s(G)$ denote the smallest integer $i$ such that the iterated line graph $L^{i}(G)$ is $s$-Hamiltonian, and let $\ell(G)$ denote the length of the longest non-closed path $P$ in which all internal vertices have degree 2 such that $P$ is not both of length 2 and in a $K_3$. …”
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Supermagic Generalized Double Graphs 1 by Ivančo Jaroslav

“…Inter alia we show that the double graphs of regular Hamiltonian graphs and some circulant graphs are supermagic.…”
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Extremal number of theta graphs of order 7 by Mohammad M. M. Jaradat, M. S. Bataineh, A. A. Al-Rhayyel, Zead Mustafa

“… For a set of graphs F , let H(n; F ) denote the class of non-bipartite Hamiltonian graphs on n vertices that does not contain any graph of F as a subgraph and h(n; F ) = max{E (G) : G E H(n; F  )} where E (G) is the number of edges in G. …”
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Akram B. Attar EXTENSIBILITY OF GRAPHS by Akram Attar

“…The class of connected graphs as well as the class of Hamiltonian graphs which are extensible classes have also been proved. …”
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Second Hamiltonian Cycles in Claw-Free Graphs by Hossein Esfandiari, Colton Magnant, Pouria Salehi Nowbandegani, Shirdareh Haghighi

“…We prove that most claw-free Hamiltonian graphs with minimum degree at least 3 have a second Hamiltonian cycle and describe the structure of those graphs not covered by our result. …”
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Akram B. Attar EXTENSIBILITY OF GRAPHS by Akram Attar

“…The class of connected graphs as well as the class of Hamiltonian graphs which are extensible classes have also been proved. …”
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Akram B. Attar EXTENSIBILITY OF GRAPHS by Akram Attar

“…The class of connected graphs as well as the class of Hamiltonian graphs which are extensible classes have also been proved. …”
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Geodesic bipancyclicity of the Cartesian product of graphs by Amruta Shinde, Y.M. Borse

“….$ In this paper, we prove that the Cartesian product of two geodesic hamiltonian graphs is a geodesic 2-bipancyclic graph. As a consequence, we show that for $n \geq 2$ every $n$-dimensional torus is a geodesic 2-bipancyclic graph.…”
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On the Implementation of Huge Random Objects by Goldreich, Oded, Goldwasser, Shafi, Nussboim, Asaf

“…For example, we consider the truthful implementation of random Hamiltonian graphs as well as supporting complex queries regarding such graphs (e.g., providing the next vertex along a fixed Hamiltonian path in such a graph).…”
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Hamiltonicity of Token Graphs of Some Join Graphs by Luis Enrique Adame, Luis Manuel Rivera, Ana Laura Trujillo-Negrete

“…We provide an infinite family of graphs, containing Hamiltonian and non-Hamiltonian graphs, for which their <i>k</i>-token graphs are Hamiltonian. …”
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