Packing of three copies of a digraph into the transitive tournament
Monika Pilśniak
Discussiones Mathematicae Graph Theory, Tome 24 (2004), p. 443-456 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)

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.

Publié le : 2004-01-01
EUDML-ID : urn:eudml:doc:270549 
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1243,
     author = {Monika Pil\'sniak},
     title = {Packing of three copies of a digraph into the transitive tournament},
     journal = {Discussiones Mathematicae Graph Theory},
     volume = {24},
     year = {2004},
     pages = {443-456},
     zbl = {1063.05111},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1243}
}

Monika Pilśniak. Packing of three copies of a digraph into the transitive tournament. Discussiones Mathematicae Graph Theory, Tome 24 (2004) pp. 443-456. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1243/

[000] [1] B. Bollobás, Extremal Graph Theory (Academic Press, London, 1978).

[001] [2] B. Bollobás and S.E. Eldridge, Packings of graphs and applications to computational complexity, J. Combin. Theory 25 (B) (1978) 105-124. | Zbl 0387.05020

[002] [3] D. Burns and S. Schuster, Every (n,n-2) graph is contained in its complement, J. Graph Theory 1 (1977) 277-279, doi: 10.1002/jgt.3190010308. | Zbl 0375.05046

[003] [4] A. Görlich, M. Pilśniak and M. Woźniak, A note on a packing problem in transitive tournaments, preprint Faculty of Applied Mathematics, University of Mining and Metallurgy, No.37/2002. | Zbl 1100.05074

[004] [5] H. Kheddouci, S. Marshall, J.F. Saclé and M. Woźniak, On the packing of three graphs, Discrete Math. 236 (2001) 197-225, doi: 10.1016/S0012-365X(00)00443-X. | Zbl 0998.05053

[005] [6] N. Sauer and J. Spencer, Edge disjoint placement of graphs, J. Combin. Theory 25 (B) (1978) 295-302. | Zbl 0417.05037

[006] [7] M. Woźniak and A.P. Wojda, Triple placement of graphs, Graphs and Combin. 9 (1993) 85-91, doi: 10.1007/BF01195330. | Zbl 0817.05034

[007] [8] M. Woźniak, Packing of graphs, Dissertationes Math. 362 (1997).

[008] [9] H.P. Yap, Some Topics in Graph Theory, London Math. Society, Lectures Notes Series, Vol. 108 (Cambridge University Press, Cambridge, 1986). | Zbl 0588.05002

[009] [10] H.P. Yap, Packing of graphs - a survey, Discrete Math. 72 (1988) 395-404, doi: 10.1016/0012-365X(88)90232-4. | Zbl 0685.05036