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Browsing by Subject "tree packing conjecture"

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    Item type:Article, Access status: Open Access ,
    Seven largest trees pack
    (Wydawnictwa AGH, 2024) Cisiński, Maciej; Żak, Andrzej
    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 packThe 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