Decomposition of (2k+1)-regular graphs containing special spanning 2k-regular Cayley graphs into paths of length 2k+1

Resumo


A Pl-decomposition of a graph G is a set of paths with l edges in G that cover the edge set of G. Favaron, Genest, and Kouider (2010) conjectured that every (2k+1)-regular graph that contains a perfect matching admits a P2k+1-decomposition. They also verified this conjecture for 5-regular graphs without cycles of length 4. In 2015, Botler, Mota, and Wakabayashi extended this result to 5-regular graphs without triangles. In this paper, we verify this conjecture for (2k+1)-regular graphs that contain the k-th power of a spanning cycle; and for 5-regular graphs that contain certain spanning 4-regular Cayley graphs.

Palavras-chave: Decomposition, regular graph, Cayley graph, path

Referências

Botler, F., Mota, G. O., Oshiro, M. T. I., and Wakabayashi, Y. (2017). Decomposing regular graphs with prescribed girth into paths of given length. Eur J Combin, 66:28–36.

Botler, F., Mota, G. O., and Wakabayashi, Y. (2015). Decompositions of triangle-free 5-regular graphs into paths of length five. Discrete Mathematics, 338(11):1845–1855.

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Favaron, O., Genest, F., and Kouider, M. (2010). Regular path decompositions of odd regular graphs. Journal of Graph Theory, 63(2):114–128.

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Publicado
30/06/2020
BOTLER, Fábio; HOFFMANN, Luiz. Decomposition of (2k+1)-regular graphs containing special spanning 2k-regular Cayley graphs into paths of length 2k+1. In: ENCONTRO DE TEORIA DA COMPUTAÇÃO (ETC), 5. , 2020, Cuiabá. Anais [...]. Porto Alegre: Sociedade Brasileira de Computação, 2020 . p. 13-16. ISSN 2595-6116. DOI: https://doi.org/10.5753/etc.2020.11078.