#### Title

Bipartite graphs and absolute difference tolerances

#### Abbreviated Journal Title

ARS Comb.

#### Keywords

COMPETITION GRAPHS; Mathematics

#### Abstract

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.

#### Journal Title

Ars Combinatoria

#### Volume

54

#### Publication Date

1-1-2000

#### Document Type

Article

#### Language

English

#### First Page

3

#### Last Page

27

#### WOS Identifier

#### ISSN

0381-7032

#### Recommended Citation

"Bipartite graphs and absolute difference tolerances" (2000). *Faculty Bibliography 2000s*. 2446.

http://stars.library.ucf.edu/facultybib2000/2446

## Comments

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