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# Amalgamations of factorizations of complete equipartite graphs.

Hilton, A. J. W. and Johnson, Matthew. (2004) 'Amalgamations of factorizations of complete equipartite graphs.', Discrete mathematics., 284 (1-3). pp. 157-175.

## Abstract

Let t be a positive integer, and let L=(l1,…,lt) and K=(k1,…,kt) be collections of nonnegative integers. A graph has a (t,K,L) factorization if it can be represented as the edge-disjoint union of factors F1,…,Ft where, for 1it, Fi is ki-regular and at least li-edge-connected. In this paper we consider (t,K,L)-factorizations of complete equipartite graphs. First we show precisely when they exist. Then we solve two embedding problems: we show when a factorization of a complete σ-partite graph can be embedded in a (t,K,L)-factorization of a complete s-partite graph, σ<s, and also when a factorization of Ka,b can be embedded in a (t,K,L)-factorization of Kn,n, a,bn. Our proofs use the technique of amalgamations of graphs.Let t be a positive integer, and let L=(l1,…,lt) and K=(k1,…,kt) be collections of nonnegative integers. A graph has a (t,K,L) factorization if it can be represented as the edge-disjoint union of factors F1,…,Ft where, for 1it, Fi is ki-regular and at least li-edge-connected. In this paper we consider (t,K,L)-factorizations of complete equipartite graphs. First we show precisely when they exist. Then we solve two embedding problems: we show when a factorization of a complete σ-partite graph can be embedded in a (t,K,L)-factorization of a complete s-partite graph, σ<s, and also when a factorization of Ka,b can be embedded in a (t,K,L)-factorization of Kn,n, a,bn. Our proofs use the technique of amalgamations of graphs.

Item Type: Article PDF - Accepted Version (260Kb) Peer-reviewed http://dx.doi.org/10.1016/j.disc.2003.11.030 07 Oct 2009 11:20 25 Nov 2011 09:40

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