Discussiones Mathematicae Graph Theory 29(3) (2009)
563-572
doi: 10.7151/dmgt.1464
Mariusz Meszka and Zdzisław Skupień
Faculty of Applied Mathematics
AGH University of Science and Technology
al. Mickiewicza 30, 30-059 Kraków, Poland
e-mail: meszka@agh.edu.pl, skupien@agh.edu.pl
Keywords: decomposition, cyclically 1-generated, remainder, surplus, universal part.
2000 Mathematics Subject Classification: 05C70, 05C20.
[1] | B. Alspach, H. Gavlas, M. Sajna and H. Verrall, Cycle decopositions IV: complete directed graphs and fixed length directed cycles, J. Combin. Theory (A) 103 (2003) 165-208, doi: 10.1016/S0097-3165(03)00098-0. |
[2] | C. Berge, Graphs and Hypergraphs (North-Holland, 1973). |
[3] | J.C. Bermond and V. Faber, Decomposition of the complete directed graph into k-circuits, J. Combin. Theory (B) 21 (1976) 146-155, doi: 10.1016/0095-8956(76)90055-1. |
[4] | J. Bosák, Decompositions of Graphs (Dordrecht, Kluwer, 1990, [Slovak:] Bratislava, Veda, 1986). |
[5] | G. Chartrand and L. Lesniak, Graphs and Digraphs (Chapman & Hall, 1996). |
[6] | A. Fortuna and Z. Skupień, On nearly third parts of complete digraphs and complete 2-graphs, manuscript. |
[7] | F. Harary and R.W. Robinson, Isomorphic factorizations X: Unsolved problems, J. Graph Theory 9 (1985) 67-86, doi: 10.1002/jgt.3190090105. |
[8] | F. Harary, R.W. Robinson and N.C. Wormald, Isomorphic factorisation V: Directed graphs, Mathematika 25 (1978) 279-285, doi: 10.1112/S0025579300009529. |
[9] | A. Kedzior and Z. Skupień, Universal sixth parts of a complete graph exist, manuscript. |
[10] | E. Lucas, Récréations Mathématiques, vol. II (Paris, Gauthier-Villars, 1883). |
[11] | M. Meszka and Z. Skupień, Self-converse and oriented graphs among the third parts of nearly complete digraphs, Combinatorica 18 (1998) 413-424, doi: 10.1007/PL00009830. |
[12] | M. Meszka and Z. Skupień, On some third parts of nearly complete digraphs, Discrete Math. 212 (2000) 129-139, doi: 10.1016/S0012-365X(99)00214-9. |
[13] | M. Meszka and Z. Skupień, Decompositions of a complete multidigraph into nonhamiltonian paths, J. Graph Theory 51 (2006) 82-91, doi: 10.1002/jgt.20122. |
[14] | M. Plantholt, The chromatic index of graphs with a spanning star, J. Graph Theory 5 (1981) 45-53, doi: 10.1002/jgt.3190050103. |
[15] | R.C. Read, On the number of self-complementary graphs and digraphs, J. London Math. Soc. 38 (1963) 99-104, doi: 10.1112/jlms/s1-38.1.99. |
[16] | Z. Skupień, The complete graph t-packings and t-coverings, Graphs Combin. 9 (1993) 353-363, doi: 10.1007/BF02988322. |
[17] | Z. Skupień, Clique parts independent of remainders, Discuss. Math. Graph Theory 22 (2002) 361, doi: 10.7151/dmgt.1181. |
[18] | Z. Skupień, Universal fractional parts of a complete graph, manuscript. |
Received 8 May 2008
Revised 22 September 2008
Accepted 13 October 2008