Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9514538 | Electronic Notes in Discrete Mathematics | 2005 | 4 Pages |
Abstract
The positive lightness of a digraph is the minimum arc value, where the value of an arc is the maximum of the in-degrees of its terminal vertices. We determine upper bounds for the positive lightness of digraphs with nonzero minimum in-degree and a given girth k⩾5 which can be embedded in a surface S. These bounds are tight for surfaces of nonnegative Euler characteristics. We further obtain bounds for classes of graphs where 3-cycles are permitted.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Stephan Dominique Andres,