Geodesic
On perfect packings in dense graphs
The electronic journal of combinatorics, Tome 20 (2013) no. 1
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We say that a graph $G$ has a perfect $H$-packing if there exists a set of vertex-disjoint copies of $H$ which cover all the vertices in $G$. We consider various problems concerning perfect $H$-packings: Given $n, r , D \in \mathbb N$, we characterise the edge density threshold that ensures a perfect $K_r$-packing in any graph $G$ on $n$ vertices and with minimum degree $\delta (G) \geq D$. We also give two conjectures concerning degree sequence conditions which force a graph to contain a perfect $H$-packing. Other related embedding problems are also considered. Indeed, we give a structural result concerning $K_r$-free graphs that satisfy a certain degree sequence condition.
DOI : 10.37236/3173
Classification : 05C70, 05C42, 05C15, 05C35
Mots-clés : subgraph packings, equitable colourings 
@article{10_37236_3173,
     author = {J\'ozsef Balogh and Alexandr Kostochka and Andrew Treglown},
     title = {On perfect packings in dense graphs},
     journal = {The electronic journal of combinatorics},
     year = {2013},
     volume = {20},
     number = {1},
     doi = {10.37236/3173},
     zbl = {1266.05115},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/3173/}
}
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József Balogh; Alexandr Kostochka; Andrew Treglown. On perfect packings in dense graphs. The electronic journal of combinatorics, Tome 20 (2013) no. 1. doi: 10.37236/3173

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