Year: 2024
Type: preprint
Abstract: We prove a conjecture of Gyárfás (1976), which asserts that any family of trees $T_1, \dots, T_{n}$ where each $T_k$ has $k$ vertices packs into $K_n$. We do so by translating the decomposition problem into a labeling problem, namely complete labeling. Our proof employs the polynomial method using a functional reformulation of the conjecture.
Source: arXiv (Cornell University)
Institution: Johns Hopkins University
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Office of Naval Research
Award: G7425413337
OpenAlex ID: W4403580151