Nondisconnecting disentanglements of amalgamated 2-factorizations of complete multipartite graphs. (English) Zbl 0994.05125

Leach, C. D.; Rodger, C. A.

J. Comb. Des. 9, No. 6, 460-467 (2001).

Summary: In this paper necessary and sufficient conditions are found for an edge-colored graph \(H\) to be the homomorphic image of a 2-factorization of a complete multipartite graph \(G\) in which each 2-factor of \(G\) has the same number of components as its corresponding color class in \(H\). This result is used to completely solve the problem of finding Hamilton decompositions of \(K_{a,b}- E(U)\) for any 2-factor \(U\) of \(K_{a,b}\).

MSC:

05C70	Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.)
05C45	Eulerian and Hamiltonian graphs
05C15	Coloring of graphs and hypergraphs

Keywords:

Hamilton cycles; amalgamation; graph homomorphism; \(m\)-cycle system; 2-factorization; multipartite graph; Hamilton decompositions

References:

[1]	Alspach, J Combin Theory B 81 pp 77– (2001) · Zbl 1023.05112 · doi:10.1006/jctb.2000.1996
[2]	and Forest leaves and 6-cycles, in preparation.
[3]	Auerbach, Discrete Math 14 pp 146– (1976)
[4]	Ph.D. dissertation, University of West Virginia, 1996.
[5]	Colbourn, Graphs Combin 2 pp 317– (1986) · Zbl 0609.05009 · doi:10.1007/BF01788106
[6]	Fu, J Graph Th 33 pp 161– (2000) · Zbl 0946.05050 · doi:10.1002/(SICI)1097-0118(200003)33:3<161::AID-JGT6>3.0.CO;2-Q
[7]	Fu, Graphs Combin
[8]	Kirkman, Cambridge and Dublin Math J 2 pp 191– (1847)
[9]	Recreations mathematiques, Vol. 2, Gauthiers Villars, Paris, 1892.
[10]	Rodger, J Graph Th 19 pp 169– (1995) · Zbl 0815.05050 · doi:10.1002/jgt.3190190205
[11]	Sajner, J Combin Theory B
[12]	Sotteau, J Combin Theory B 30 pp 75– (1981) · Zbl 0463.05048 · doi:10.1016/0095-8956(81)90093-9
[13]	de Werra, Rev. Francaise Informat. Recherche Operationnelle 5 pp 1– (1971)
[14]	Introduction to graph theory, Prentice-Hall, Upper Saddle River, NJ, 1996. · Zbl 0891.05001