Year: 2025
Type: preprint
Abstract: A $k$-star decomposition of a graph is a partition of its edges into $k$-stars (i.e., $k$ edges with a common vertex). The paper studies the following problem: given $k \leq d/2$, does the random $d$-regular graph have a $k$-star decomposition (asymptotically almost surely, provided that the number of edges is divisible by $k$)? Delcourt, Greenhill, Isaev, Lidický, and Postle proved the a.a.s. existence for every odd $k$ using earlier results regarding orientations satisfying certain degree conditions modulo $k$. In this paper we give a direct, self-contained proof that works for every $d$ and every $k
Source: arXiv (Cornell University)
Author: Harangi, Viktor
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G4053845998
OpenAlex ID: W4416138650
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