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Browsing by Subject "packing"

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  • thumbnail.journal.alt
    Item type:Article, Access status: Open Access ,
    2-biplacement without fixed points of (p,q)-bipartite graphs
    (2005) Orchel, Beata
    In this paper we consider 2-biplacement without fixed points of paths and $(p, q)$-bipartite graphs of small size. We give all $(p, q)$-bipartite graphs $G$ of size q for which the set $\mathcal{S}^{*}(G)$ of all 2-biplacements of $G$ without fixed points is empty.
  • thumbnail.journal.alt
    Item type:Thesis, Access status: Restricted ,
    Hipoteza Erdősa-Sós
    (Data obrony: 2009-10-15) Pieczka, Marcelina
    Wydział Matematyki Stosowanej
  • thumbnail.journal.alt
    Item type:Thesis, Access status: Restricted ,
    Podziały krawędziowe grafów gęstych
    (Data obrony: 2018-07-16) Hubert, Maciej
    Wydział Matematyki Stosowanej
  • thumbnail.journal.alt
    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
  • thumbnail.journal.alt
    Item type:Article, Access status: Open Access ,
    Toward Wojda's conjecture on digraph packing
    (Wydawnictwa AGH, 2017) Konarski, Jerzy; Żak, Andrzej
    Given a positive integer $m\leq n/2$, Wojda conjectured in 1985 that if $D_1$ and $D_2$ are digraphs of order n such that $|A(D_1)|\leq n−m$ and $|A(D_2)|\leq 2n-\lfloor n/m\rfloor-1$ then $D_1$ and $D_2$ pack. The cases when $m=1$ or $m=n/2$ follow from known results. Here we prove the conjecture for $m\geq\sqrt{8n}+418275$.