Highly Influenced

# The competition number of a graph and the dimension of its hole space

@article{Kim2012TheCN, title={The competition number of a graph and the dimension of its hole space}, author={Suh-Ryung Kim and Jung Yeun Lee and Boram Park and Yoshio Sano}, journal={Appl. Math. Lett.}, year={2012}, volume={25}, pages={638-642} }

- Published 2012 in Appl. Math. Lett.
DOI:10.1016/j.aml.2011.10.003

The competition graph of a digraph D is a (simple undirected) graph which has the same vertex set as D and has an edge between x and y if and only if there exists a vertex v in D such that (x, v) and (y, v) are arcs of D. For any graph G, G together with sufficiently many isolated vertices is the competition graph of some acyclic digraph. The competition number k(G) of G is the smallest number of such isolated vertices. In general, it is hard to compute the competition number k(G) for a graph G… CONTINUE READING