Guilherme Oliveira Mota

Decompositions of triangle-free 5-regular graphs into paths of length five

A P k -decomposition of a graph? G is a set of edge-disjoint paths with k ?edges that cover the edge set of? G . Kotzig (1957) proved that a?3-regular graph admits a P 3 -decomposition if and only if it contains a perfect matching. Kotzig also asked what are the necessary and sufficient conditions for a ( 2 k + 1 ) -regular graph to admit a decomposition into paths with 2 k + 1 ?edges. We partially answer this question for the case k = 2 by proving that the existence of a perfect matching is sufficient for a triangle-free 5-regular graph to admit a P 5 -decomposition. This result contributes positively to the conjecture of Favaron et?al. (2010) that states that every? ( 2 k + 1 ) -regular graph with a perfect matching admits a P 2 k + 1 -decomposition.

Loose Hamiltonian Cycles Forced by Large

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Decomposing highly connected graphs into paths of length five

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Path decompositions of regular graphs with prescribed girth

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On an anti-Ramsey property of random graphs

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Decompositions of highly connected graphs into paths of any given length

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Monochromatic trees in random graphs

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Loose Hamiltonian cycles forced by large (k − 2)-degree - sharp version☆

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