If X is a connected graph, then an X-factor of a larger graph is a spanning subgraph in which all of its components are isomorphic to X. Given a set Γ of pairwise non-isomorphic graphs, a uniformly resolvable Γ-decompositionof a graph G is an edge decomposition of G into X-factors for some graph X ∈ Γ. In this article we completely solve the existence problem for decompositions of K_v-I into Cn-factors and K_1,n-factors in the case when n is even.
Uniformly resolvable decompositions of Kv-I into n-cycles and n-stars, for even n
G. Lo Faro;A. Tripodi
2020-01-01
Abstract
If X is a connected graph, then an X-factor of a larger graph is a spanning subgraph in which all of its components are isomorphic to X. Given a set Γ of pairwise non-isomorphic graphs, a uniformly resolvable Γ-decompositionof a graph G is an edge decomposition of G into X-factors for some graph X ∈ Γ. In this article we completely solve the existence problem for decompositions of K_v-I into Cn-factors and K_1,n-factors in the case when n is even.File in questo prodotto:
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Uniformly Resolvable Decompositions of K_v-I into n-cycles and n-stars, for even n .pdf
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