TY  - JOUR
ID  - Cisiński2024
LB  - Cisiński2024
AU  - Cisiński, Maciej
AU  - Żak, Andrzej
TI  - Seven largest trees pack
ST  - Seven largest trees pack
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2024
VL  - 44
IS  - 5
SP  - 673
EP  - 688
DO  - https://doi.org/10.7494/OpMath.2024.44.5.673
UR  - https://doi.org/10.7494/OpMath.2024.44.5.673
AB  - The Tree Packing Conjecture (TPC) by Gyárfás states that any set of trees \(T_2,\dots,T_{n-1}, T_n\) such that \(T_i\) has \(i\) vertices pack into \(K_n\). The conjecture is true for bounded degree trees, but in general, it is widely open. Bollobás proposed a weakening of TPC which states that \(k\) largest trees pack. The latter is true if none tree is a star, but in general, it is known only for \(k=5\). In this paper we prove, among other results, that seven largest trees pack.
KW  - tree
KW  - packing
KW  - tree packing conjecture
SN  - 1232-9274
ER  -