Abstract: A decomposition of a graph G is a collection ψ of subgraphs H1,H2, . . . , Hr of G such that every edge of G belongs to exactly one Hi. If each Hi is either an induced path or an induced cycle in G, then ψ is called an induced path decomposition of G. The minimum cardinality of an induced path decomposition of G is called the induced path decomposition number of G and is denoted by πi(G). In this paper we initiate a study of this parameter.
Abstract: A decomposition of a graph G is a collection ψ of
graphs H1,H2, . . . , Hr of G such that every edge of G belongs
to exactly one Hi. If each Hi is either an induced path in G,
then ψ is called an induced acyclic path decomposition of G and
if each Hi is a (induced) cycle in G then ψ is called a (induced)
cycle decomposition of G. The minimum cardinality of an induced
acyclic path decomposition of G is called the induced acyclic path
decomposition number of G and is denoted by ¤Çia(G). Similarly
the cyclic decomposition number ¤Çc(G) is defined. In this paper we
begin an investigation of these parameters.