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Justyna Otfinowska, Mariusz Woźniak (2013)
Discussiones Mathematicae Graph Theory
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Let F be a forest of order n. It is well known that if F 6= Sn, a star of order n, then there exists an embedding of F into its complement F. In this note we consider a problem concerning the uniqueness of such an embedding.
Martin Loebl, Svatopluk Poljak (1988)
Mathematica Slovaca
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Görlich, Agnieszka, Żak, Andrzej (2009)
The Electronic Journal of Combinatorics [electronic only]
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David Offner (2014)
Discussiones Mathematicae Graph Theory
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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.
András Gyárfás (2014)
Discussiones Mathematicae Graph Theory
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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.
Janata, Marek, Loebl, Martin, Szabó, Jácint (2005)
The Electronic Journal of Combinatorics [electronic only]
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Caro, Yair, Yuster, Raphael (1997)
The Electronic Journal of Combinatorics [electronic only]
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Daouya Laïche, Isma Bouchemakh, Éric Sopena (2017)
Discussiones Mathematicae Graph Theory
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The packing chromatic number χρ(G) of a graph G is the smallest integer k such that its set of vertices V(G) can be partitioned into k disjoint subsets V1, . . . , Vk, in such a way that every two distinct vertices in Vi are at distance greater than i in G for every i, 1 ≤ i ≤ k. For a given integer p ≥ 1, the p-corona of a graph G is the graph obtained from G by adding p degree-one neighbors to every vertex of G. In this paper, we determine the packing chromatic number of p-coronae...