Constructing all Possible Leaves for Maximum Packings of the Complete Graph with Stars of Sizes Six and Seven

Major

Mathematics

Submission Type

Poster

Area of Study or Work

Mathematics

Expected Graduation Date

2023

Location

CNS Atrium, Easel 18

Start Date

4-15-2023 10:30 AM

End Date

4-15-2023 11:45 AM

Abstract

A 6-star is the complete bipartite graph K1,6. A packing of Kn with 6-stars is a set of edge disjoint subgraphs of Kn, each of which is isomorphic to S6. The set of edges of Kn which are not used in the packing is called the leave and is denoted by L. The packing is called maximum if |L| is minimum with respect to all such packings. We show that every possible leave graph is achievable as the leave of a maximum packing of Kn with 6-stars and 7-stars.

This document is currently not available here.

Share

COinS
 
Apr 15th, 10:30 AM Apr 15th, 11:45 AM

Constructing all Possible Leaves for Maximum Packings of the Complete Graph with Stars of Sizes Six and Seven

CNS Atrium, Easel 18

A 6-star is the complete bipartite graph K1,6. A packing of Kn with 6-stars is a set of edge disjoint subgraphs of Kn, each of which is isomorphic to S6. The set of edges of Kn which are not used in the packing is called the leave and is denoted by L. The packing is called maximum if |L| is minimum with respect to all such packings. We show that every possible leave graph is achievable as the leave of a maximum packing of Kn with 6-stars and 7-stars.