-colorings and -bipartite graphs.
-adic analysis and Bell numbers of two variables. (Analyse -adique et nombres de Bell à deux variables.)
-adic analysis and classical sequences of numbers. (Analyse -adique et suites classiques de nombres.)
-partitions and a multi-parameter Klyachko idempotent.
and line-transitive linear spaces.
(3) as a symmetric (36, 15, 6)-design
Packing 10 or 11 unit squares in a square.
Packing densities of patterns.
Packing four copies of a tree into a complete bipartite graph
In considering packing three copies of a tree into a complete bipartite graph, H. Wang (2009) gives a conjecture: For each tree of order and each integer , there is a -packing of in a complete bipartite graph whose order is . We prove the conjecture is true for .
Packing graphs: The packing problem solved.
Packing independent sets and transversals
Packing of 180 equal circles on a sphere.
Packing of graphs [Book]
Packing of nonuniform hypergraphs - product and sum of sizes conditions
Hypergraphs of order n are mutually packable if one can find their edge disjoint copies in the complete hypergraph of order n. We prove that two hypergraphs are mutually packable if the product of their sizes satisfies some upper bound. Moreover we show that an arbitrary set of the hypergraphs is mutually packable if the sum of their sizes is sufficiently small.
Packing of three copies of a digraph into the transitive tournament
In this paper, we show that if the number of arcs in an oriented graph G (of order n) without directed cycles is sufficiently small (not greater than [2/3] n-1), then there exist arc disjoint embeddings of three copies of G into the transitive tournament TTₙ. It is the best possible bound.
Packing Parameters in Graphs
In a graph G = (V,E), a non-empty set S ⊆ V is said to be an open packing set if no two vertices of S have a common neighbour in G. An open packing set which is not a proper subset of any open packing set is called a maximal open packing set. The minimum and maximum cardinalities of a maximal open packing set are respectively called the lower open packing number and the open packing number and are denoted by ρoL and ρo. In this paper, we present some bounds on these parameters.
Packing patterns into words.
Packing the Hypercube
Let G be a graph that is a subgraph of some n-dimensional hypercube Qn. For sufficiently large n, Stout [20] proved that it is possible to pack vertex- disjoint copies of G in Qn so that any proportion r < 1 of the vertices of Qn are covered by the packing. We prove an analogous theorem for edge-disjoint packings: For sufficiently large n, it is possible to pack edge-disjoint copies of G in Qn so that any proportion r < 1 of the edges of Qn are covered by the packing.
Packing Trees Into n-Chromatic Graphs
We show that if a sequence of trees T1, T2, ..., Tn−1 can be packed into Kn then they can be also packed into any n-chromatic graph.
Packing unit squares in squares: A survey and new results.