Completing Partial k‐Star Designs
ABSTRACT A ‐star is a complete bipartite graph . A partial ‐star design of order is a pair where is a set of vertices and is a set of edge‐disjoint ‐stars whose vertex sets are subsets of . If each edge of the complete graph with vertex set is in some star in , then is a (complete) ‐star design . We say that is completable if there is a ‐star design such that . In this paper we determine, for all and , the minimum number of stars in an uncompletable partial ‐star design of order .
Authors
- Daniel Horsley (ORCID: https://orcid.org/0000-0001-9971-7148)
- Ajani De Vas Gunasekara (ORCID: https://orcid.org/0000-0002-2404-0344)
Institutions
- Monash University (AU)
- The University of Notre Dame Australia (AU)
Publication Details
- Journal
- Journal of Combinatorial Designs
- Published
- 2025-08-17
- DOI
- https://doi.org/10.1002/jcd.22003
- Primary Topic
- graph theory and CDMA systems
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- University of Notre Dame
- Monash University
- University of Notre Dame Australia