Results 31 to 40 of about 2,059,443 (151)
The parity Hamiltonian cycle problem
Discrete Mathematics, 2018 Motivated by a relaxed notion of the celebrated Hamiltonian cycle, this paper investigates its variant, parity Hamiltonian cycle (PHC): A PHC of a graph is a closed walk which visits every vertex an odd number of times, where we remark that the walk may use an edge more than once. First, we give a complete characterization of the graphs which have PHCs,
Hiroshi Nishiyama +4 more
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On Cyclic Near-Hamiltonian Cycle System of the Complete Multigraph
, 2017 cycle system of Kv is Hamiltonian when each of its cycles passes through all vertices of v K .In this paper, we propose a new type of cycle system called near-Hamiltonian cycle system of v K which has all its cycles of length v 1. We are concerned with a
Ibrahim, Haslinda, Aldiabat, Raja'i
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Hamiltonian Chains in Hypergraphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2005 Hamiltionian chain is a generalisation of hamiltonian cycles for hypergraphs. Among the several possible ways of generalisations this is probably the most strong one, it requires the strongest structure.
Gyula Y. Katona
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Problems on Shortest k-Node Cycles and Paths
Кібернетика та комп'ютерні технології, 2021 The paper is devoted to the construction of mathematical models for problems on the shortest cycles and paths, that pass through a given number of nodes of a directed graph.
Petro Stetsyuk +2 more
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Hamiltonian cycles in torical lattices [PDF]
Discrete Mathematics & Theoretical Computer Science, 2005 We establish sufficient conditions for a toric lattice $T_{m,n}$ to be Hamiltonian. Also, we give some asymptotics for the number of Hamiltonian cycles in $T_{m,n}$.
Vladimir K. Leontiev
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Removable matchings and hamiltonian cycles
Discrete Mathematics, 2009 The authors show the following two results: {\parindent=5mm \begin{itemize}\item[1)]Let \(G\) be a graph of order \(n\geq 4k+3\) with \(\sigma_2 (G)\geq n\) and let \(F\) be a matching of size \(k\) in \(G\) such that \(G-F\) is 2-connected. Then \(G-F\) is hamiltonian or \(G\cong K_2 +(K_2\cup K_{n-4})\) or \(G\cong \bar{K_2} +(K_2\cup K_{n-4 ...
Zhiquan Hu, Hao Li
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The Parity of Directed Hamiltonian Cycles [PDF]
2013 IEEE 54th Annual Symposium on Foundations of Computer Science, 2013 We present a deterministic algorithm that given any directed graph on n vertices computes the parity of its number of Hamiltonian cycles in O(1.619^n) time and polynomial space. For bipartite graphs, we give a 1.5^n poly(n) expected time algorithm. Our algorithms are based on a new combinatorial formula for the number of Hamiltonian cycles modulo a ...
Björklund, Andreas, Husfeldt, Thore
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Alternating Hamiltonian cycles in $2$-edge-colored multigraphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2019 A path (cycle) in a $2$-edge-colored multigraph is alternating if no two consecutive edges have the same color. The problem of determining the existence of alternating Hamiltonian paths and cycles in $2$-edge-colored multigraphs is an $\mathcal{NP ...
Alejandro Contreras-Balbuena +2 more
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Hamiltonian Spider Intersection Graphs Are Cycle Extendable
, 2013 A cycle $C$ in a graph is extendable if there exists a cycle $C\u27$ such that $V(C) \subseteq V(C\u27)$ and $|V(C\u27)|$ = $|V(C)|$ + 1. A graph is cycle extendable if every non-Hamiltonian cycle in the graph is extendable.
Busch, Arthur +2 more
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