Hilton, A. J. W. &
Johnson, Matthew. (2004). Amalgamations of factorizations of complete equipartite graphs.
Discrete Mathematics 284(1-3): 157-175.
Author(s) from Durham
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
i=1,...,
t
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. Our proofs use the technique of amalgamations of graphs.
