On the packing of two copies of a caterpillar in its third power

• Autorzy: Christian Germain , Hamamache Kheddouci
• Języki publikacji: EN

Abstrakty

EN

H. Kheddouci, J.F. Saclé and M. Woźniak conjectured in 2000 that if a tree T is not a star, then there is an edge-disjoint placement of T into its third power.In this paper, we prove the conjecture for caterpillars.

Słowa kluczowe

EN

packing; placement; permutation; power of tree; caterpillar

Kategorie tematyczne

• 05C05: Trees
• 05C70: Factorization, matching, partitioning, covering and packing

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2003
• Tom: 23
• Numer: 1
• Strony: 105-115

Daty

wydano

2003

otrzymano

2001-07-10

poprawiono

2002-07-05

Twórcy

autor

Christian Germain

• LE2I, FRE-CNRS 2309, Université de Bourgogne, B.P. 47870, 21078 Dijon Cedex, France

autor

Hamamache Kheddouci

• LE2I, FRE-CNRS 2309, Université de Bourgogne, B.P. 47870, 21078 Dijon Cedex, France

Bibliografia

• [1] B. Bollobás, Extremal Graph Theory (Academic Press, London, 1978).
• [2] S. Brandt, Embedding graphs without short cycles in their complements, in: Y. Alavi and A. Schwenk, eds., Graph Theory, Combinatorics, and Applications of Graphs, Vol. 1 (John Wiley and Sons, 1995), 115-121.
• [3] D. Burns and S. Schuster, Every (p,p-2) graph is contained in its complement, J. Graph Theory 1 (1977) 277-279, doi: 10.1002/jgt.3190010308.
• [4] S.M. Hedetniemi, S.T. Hedetniemi and P.J. Slater, A note on packing two trees into $K_N$, Ars Combin. 11 (1981) 149-153.
• [5] H. Kheddouci, Packing of some trees into their third power, to appear in Appl. Math. Letters.
• [6] H. Kheddouci, J.F. Saclé and M. Woźniak, Packing of two copies of a tree into its fourth power, Discrete Math. 213 (2000) 169-178, doi: 10.1016/S0012-365X(99)00177-6.
• [7] N. Sauer and J. Spencer, Edge disjoint placement of graphs, J. Combin. Theory (B) 25 (1978) 295-302, doi: 10.1016/0095-8956(78)90005-9.
• [8] H. Wang and N. Sauer, Packing three copies of a tree into a complete graph, Europ. J. Combin. 14 (1993) 137-142, doi: 10.1006/eujc.1993.1018.
• [9] M. Woźniak, A note on embedding graphs without small cycles, Colloq. Math. Soc. J. Bolyai 60 (1991) 727-732.
• [10] M. Woźniak, Packing of Graphs, Dissertationes Math. CCCLXII (1997) pp. 78.
• [11] H.P. Yap, Some Topics in Graph Theory, London Mathematical Society, Lectures Notes Series 108 (Cambridge University Press, Cambridge, 1986).

Identyfikatory

DOI

10.7151/dmgt.1188