Abstract Let H be a family of t-sets on {l,2, …, k }. A family of k-sets on v elements is called a (v, k, ϰ)-packing if for all F ∈ there is a copy of ϰ, ϰ F such that the t-sets of F corresponding to H F are covered only by F.
P. Frankl, Z. Füredi
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Packing Densities of Colored and Non-Colored Patterns
GS4 Student Scholars Symposium 2015, 2015Pattern packing concerns finding an optimal permutation that contains the maximum number of occurrences of a given pattern and computing the corresponding packing density. In many instances such an optimal permutation can be characterized directly and the number of occurrences of the pattern in interest may be enumerated explicitly. In more complicated
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Algebraic and Combinatorial Algorithms for S-Packing Coloring
ACM Communications in Computer AlgebraS -packing coloring is a generalization of proper coloring of graphs, introduced more than a decade ago. In this paper, we present algebraic and combinatorial algorithms for the problem of S -packing coloring of finite undirected and unweighted graphs. We assess the upper bounds for the complexity of our
K. Mohamed Harith +2 more
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Colored Bin Packing: Online Algorithms and Lower Bounds
Algorithmica, 2016zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Martin Böhm 0001 +4 more
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Note on packing patterns in colored permutations
Online Journal of Analytic Combinatorics, 2016Packing patterns in permutations concerns finding the permutation with the maximum number of a prescribed pattern. In 2002, Albert, Atkinson, Handley, Holton and Stromquist showed that there always exists a layered permutation containing the maximum number of a layered pattern among all permutations of length n. Consequently the packing density for all
Just, Matthew, Wang, Hua
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\((d, n)\)-packing colorings of infinite lattices
Discret. Appl. Math., 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Danilo Korze, Aleksander Vesel
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A set packing model for the Partition Coloring Problem
Carpathian Journal of MathematicsIn this paper we propose a set packing model for the Partition Coloring Problem (PCP) a gener alization of the Vertex Coloring Problem (VCP). Given a graph whose vertex set is partitioned in clusters, PCP aims to select one vertex from each cluster such that the chromatic number of the resulted induced subgraph is minimal.
Olariu, Emanuel Florentin +1 more
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Covering, Coloring, and Packing Hypergraphs
2017A hypergraph \(\mathcal {H}=(\mathcal V,\mathcal E)\) consists of a (finite) vertex set \(\mathcal V\) and a set of hyper-edges \(\mathcal E\), where each edge \(E\in \mathcal E\) is a subset of \(E\subset \mathcal V\). The vertices will usually be labelled by \(\mathcal V=(v_1,\dots ,v_I)\), the edges by \(\mathcal E=(E_1,\dots ,E_J)\), where \(I,J\in
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Packing ( 1 , 1 , 2 , 4 ) -coloring of subcubic outerplanar graphs
Discrete Applied Mathematics, 2021Alexandr Kostochka, Xujun Liu
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