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Acta Math. Hung. 42 (3----4)(1983), 221--223.
 

Summary: Acta Math. Hung.
42 (3----4)(1983), 221--223.
A NOTE ON THE DECOMPOSITION OF GRAPHS
INTO ISOMORPHIC MATCHINGS
N. ALON (Cambridge)
All graphs considered are finite, undirected, with no loops and no multiple
edges. A graph H is said to have a G-decomposition if it is the union of pairwise
edge-disjoint subgraphs each isomorphic to G. We denote this situation by GIH.
Many results are known about G-decomposition, for references see e.g. [1]
and [6]. In this paper we establish some necessary and sufficient conditions for
a graph H to have a tK2-decomposition, where tK2 is the graph consisting of
t independent edges. Our result implies, as a very special case, the main result
of Bialostocki and Roditty [3], that states that if G is a graph with e edges and
maximum degree A, then, with a finite number of exceptions, 3K2IG iff 3le
and A<=e/3.
For every graph G, E(G) is the set of edges of G and e(G)= IE(G)I. //(63
is the maximum degree of G and z'(G) is the chromatic index (=edge-chromatic
number) of G.
We begin with the following simple lemma, which is proved in [2]:
LEMMA1. Let G be a graph and let M, NcE(G) be disjoint matchings of

  

Source: Alon, Noga - School of Mathematical Sciences, Tel Aviv University

 

Collections: Mathematics