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Identifying Hamilton cycles in the Cartesian product of directed cycles
AKCE International Journal of Graphs and Combinatorics, 2020 Let be a Cartesian product of directed cycles. It is known that has a Hamilton cycle if there is a permutation of that satisfies and for some positive integers , where . In addition, if then has two arc-disjoint Hamilton cycles.
Zbigniew R. Bogdanowicz
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On Implicit Heavy Subgraphs and Hamiltonicity of 2-Connected Graphs
Discussiones Mathematicae Graph Theory, 2021 A graph G of order n is implicit claw-heavy if in every induced copy of K1,3 in G there are two non-adjacent vertices with sum of their implicit degrees at least n. We study various implicit degree conditions (including, but not limiting to, Ore- and Fan-
Zheng Wei, Wideł Wojciech, Wang Ligong
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Well-spread sequences and edge-labellings with constant Hamilton-weight [PDF]
Discrete Mathematics & Theoretical Computer Science, 2004 A sequence (a_i) of integers is \emphwell-spread if the sums a_i+a_j, for ...
Peter Mark Kayll
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Finding Hamilton cycles in random intersection graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2018 The construction of the random intersection graph model is based on a random family of sets. Such structures, which are derived from intersections of sets, appear in a natural manner in many applications. In this article we study the problem of finding a
Katarzyna Rybarczyk
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A Note Concerning Hamilton Cycles in Some Classes of Grid Graphs
Journal of Mathematical and Fundamental Sciences, 2013 A graph G is called hamiltonian if it contains a Hamilton cycle, i.e. a cycle containing all vertices. Deciding whether a given graph has a Hamilton cycle is an NP-complete problem. But, it is a polynomial problem within some special graph classes.
A. N.M. Salman +2 more
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Difference divisor graph of the finite group [PDF]
International Journal of Research in Industrial Engineering, 2018 Let (Zn, +) be a finite group of integers modulo n and Dn a non-empty subset of Zn containing proper devisors of n. In this paper, we have introduced the difference divisor graph Diff (Zn, Dn) associated with Zn whose vertices coincide with Zn such that ...
R. V M S S Kiran Kumar, T. Chalapathi
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Families of triples with high minimum degree are hamiltonian
Discussiones Mathematicae Graph Theory, 2014 In this paper we show that every family of triples, that is, a 3-uniform hypergraph, with minimum degree at least contains a tight Hamiltonian ...
Rödl Vojtech, Ruciński Andrzej
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Matchings and Hamilton cycles in hypergraphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2005 It is well known that every bipartite graph with vertex classes of size $n$ whose minimum degree is at least $n/2$ contains a perfect matching. We prove an analogue of this result for uniform hypergraphs. We also provide an analogue of Dirac's theorem on
Daniela Kühn, Deryk Osthus
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Hamilton Cycles in Double Generalized Petersen Graphs
Discussiones Mathematicae Graph Theory, 2019 Coxeter referred to generalizing the Petersen graph. Zhou and Feng modified the graphs and introduced the double generalized Petersen graphs (DGPGs). Kutnar and Petecki proved that DGPGs are Hamiltonian in special cases and conjectured that all DGPGs are
Sakamoto Yutaro
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Removable Edges on a Hamilton Cycle or Outside a Cycle in a 4-Connected Graph
Discussiones Mathematicae Graph Theory, 2021 Let G be a 4-connected graph. We call an edge e of G removable if the following sequence of operations results in a 4-connected graph: delete e from G; if there are vertices with degree 3 in G− e, then for each (of the at most two) such vertex x, delete ...
Wu Jichang +3 more
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