On the ascending star subgraph decomposition of star forests

Abstract

LetG be a graph of size\(\left( {n_2^ + 1} \right)\) for some integern≥2. ThenG is said to have an ascending star subgraph decomposition ifG can be decomposed inton subgraphsG 1,G 2, ...,G n such that eachG i is a star of sizei with 1≤in. We shall prove in this paper that a star forest with size\(\left( {n_2^ + 1} \right)\), possesses an ascending star subgraph decomposition if the size of each component is at leastn, which is stronger than the conjecture proposed by Y. Alavi, A. J. Boals, G. Chartrand, P. Erdős and O. R. Oellermann.

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Ma, K., Zhou, H. & Zhou, J. On the ascending star subgraph decomposition of star forests. Combinatorica 14, 307–320 (1994). https://doi.org/10.1007/BF01212979

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