Bipartite graphs and absolute difference tolerances
Abbreviated Journal Title
COMPETITION GRAPHS; Mathematics
An abdiff-tolerance competition graph, G = (V, E), is a graph for which each vertex i can be assigned a non-negative integer ti and at most \V\ subsets S-j of V can be found such that xy E E if and only if x and y lie in at least \t(x)-t(y)\ of the sets S-j. If G is not an abdiff-tolerance competition graph, it still is possible to find r > \V\ subsets of V having the above property. The integer r - \V\ is called the abdiff-tolerance competition number. This paper determines those complete bipartite graphs which are abdiff-tolerance competition graphs and finds an asymptotic value for the abdiff-tolerance competition number of K-l,K-n.
"Bipartite graphs and absolute difference tolerances" (2000). Faculty Bibliography 2000s. 2446.