Acyclic graphoidal covers and path partitions in a graph

@article{Arumugam1998AcyclicGC,
title={Acyclic graphoidal covers and path partitions in a graph},
author={S. Arumugam and J. Suresh Suseela},
journal={Discrete Mathematics},
year={1998},
volume={190},
pages={67-77}
}

An acyclic graphoidal cover of a graph G is a collection $ of paths in G such that every path in $ has at least two vertices, every vertex of G is an internal vertex of at most one path in ~/and every edge of G is in exactly one path in $. The minimum cardinality of an acyclic graphoidal cover of G is called the aeyclie graphoidal covering number of G and is denoted by ~/a. A path partition of a graph G is a collection ~ of paths in G such that every edge of G is in exactly one path in ~ . The… CONTINUE READING