Elsevier

Discrete Mathematics

Volume 244, Issues 1–3, 6 February 2002, Pages 83-94
Discrete Mathematics

Regular packings of regular graphs

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Abstract

A graph H is G-decomposable if it contains subgraphs G1,…,Gh,h⩾2, isomorphic to G whose sets of edges partition E(H). Wilson (Proceedings of the Fifth British Combinatorial Conference, University of Aberdeen, Aberdeen, 1975, pp. 647–659; Congr. Numer. XV, Utilitas, Math., Winnipeg, Manitoba, 1976) proved that, given a nonempty graph G, the complete graph KN is G-decomposable for N large enough, provided some natural divisibility conditions hold. Fink and Ruiz (Czechoslovak Math. J. 36 (111) (1986) 172) proved that a noncomplete G-decomposable graph H exists even within the class of circulant graphs. The order N0(G) of the smallest G-decomposable regular graph is known only for particular classes of graphs or for graphs with small maximum degree. We give some tools to study the problem of determining N0(G) when G is a connected regular graph. These tools are applied to obtain upper and lower bounds of N0(G) for regular graphs of degree r⩾|V(G)|/2. Families of extremal graphs which attain the bounds are also given.

Keywords

Graph decomposition
Packing

Cited by (0)

Work supported by the Spanish Research Council CICYT under project TIC-97-0963, and the Catalan Research Council under grant 1998 SGR00119.

1

Departamento de Matemáticas, Universidad Central de Las Villas, Cuba.