Antwan Clark

collaborators

2 papers

math.CO2024

Every tree on $n$ edges decomposes $K_{n x, n x}$ and $K_{2 n x + 1}$

Parikshit Chalise, Antwan Clark, Edinah K. Gnang

We prove that every tree on $n$ edges decomposes $K_{n x, n x}$ and $K_{2 n x + 1}$ for all positive integers $x$ . The said decompositions are obtained by proving that every tree admits…

math.CO2024

A Proof of the Tree Packing Conjecture

Parikshit Chalise, Antwan Clark, Edinah K. Gnang

We prove a conjecture of GyÃ¡rfÃ¡s (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 th…

Every tree on n edges decomposes Knx,nx​ and K2nx+1​

A Proof of the Tree Packing Conjecture

Every tree on $n$ edges decomposes $K_{n x, n x}$ and $K_{2 n x + 1}$