Let 1 ≤ a < b be integers and G a graph of order n sufficiently large for a and b. Then G has an [ a, b ]-factor if the minimum degree is at least a and every pair of vertices distance two apart has cardinality of the neighborhood union at least an / ( a + b ). This lower bound is sharp. As a consequence, we have a Fan-type condition for a graph to have an [ a, b ]-factor.
- [ a, b ]-factor
- Neighborhood union
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics
- Theoretical Computer Science