Uniformly resolvable decompositions of $K_v$ into one $1$-factor and $n$-stars when $n>1$ is odd

Jehyun Lee; Melissa Keranen

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arXiv · 2504.15142

Uniformly resolvable decompositions of $K_v$ into one $1$-factor and $n$-stars when $n>1$ is odd

Jehyun Lee·Melissa Keranen

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Abstract

We consider uniformly resolvable decompositions of $K_v$ into subgraphs such that each resolution class contains only blocks isomorphic to the same graph. We give a complete solution for the case in which one resolution class is $K_2$ and the rest are $K_{1,n}$ where $n>1$ is odd.

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Jehyun Lee, Melissa Keranen. 2025-04-21. Uniformly resolvable decompositions of $K_v$ into one $1$-factor and $n$-stars when $n>1$ is odd. https://arxiv.org/abs/2504.15142

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