Alspach's problem: The case of Hamilton cycles and 5-cycles.
Jordon, Heather (2011)
The Electronic Journal of Combinatorics [electronic only]
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Jordon, Heather (2011)
The Electronic Journal of Combinatorics [electronic only]
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Shanmugasundaram Jeevadoss, Appu Muthusamy (2015)
Discussiones Mathematicae Graph Theory
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We give necessary and sufficient conditions for the decomposition of complete bipartite multigraph Km,n(λ) into paths and cycles having k edges. In particular, we show that such decomposition exists in Km,n(λ), when λ ≡ 0 (mod 2), [...] and k(p + q) = 2mn for k ≡ 0 (mod 2) and also when λ ≥ 3, λm ≡ λn ≡ 0(mod 2), k(p + q) =λ_mn, m, n ≥ k, (resp., m, n ≥ 3k/2) for k ≡ 0(mod 4) (respectively, for k ≡ 2(mod 4)). In fact, the necessary conditions given above are also sufficient when λ =...
T. Pezda (2004)
Open Mathematics
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We find all possible cycle-lengths for polynomial mappings in two variables over rings of integers in quadratic extensions of rationals.
Paul A. White (1950)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Marcus Nilsson (2000)
Annales mathématiques Blaise Pascal
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Smith, Benjamin R. (2009)
The Electronic Journal of Combinatorics [electronic only]
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Nathanson, Melvyn B., Sullivan, Blair D. (2008)
Integers
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Meszka, Mariusz (2009)
The Electronic Journal of Combinatorics [electronic only]
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Atif A. Abueida, Chester Lian (2014)
Discussiones Mathematicae Graph Theory
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Let Cm and Sm denote a cycle and a star on m edges, respectively. We investigate the decomposition of the complete graphs, Kn, into cycles and stars on the same number of edges. We give an algorithm that determines values of n, for a given value of m, where Kn is {Cm, Sm}-decomposable. We show that the obvious necessary condition is sufficient for such decompositions to exist for different values of m.
Fleming, Thomas, Diesl, Alexander (2005)
Algebraic & Geometric Topology
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