Leaves for packings with block size four
| dc.contributor.author | Chang, Yanxun | |
| dc.contributor.author | Dukes, Peter J. | |
| dc.contributor.author | Feng, Tao | |
| dc.date.accessioned | 2021-03-01T23:58:45Z | |
| dc.date.available | 2021-03-01T23:58:45Z | |
| dc.date.copyright | 2019 | en_US |
| dc.date.issued | 2019 | |
| dc.description.abstract | We consider maximum packings of edge-disjoint 4-cliques in the complete graph Kn. When n 1 or 4 (mod 12), these are simply block designs. In other congruence classes, there are necessarily uncovered edges; we examine the possible ‘leave’ graphs induced by those edges. We give particular emphasis to the case n 0 or 3 (mod 12), when the leave is 2-regular. Colbourn and Ling settled the case of Hamiltonian leaves in this case. We extend their construction and use several additional direct and recursive constructions to realize a variety of 2-regular leaves. For various subsets S {3, 4, 5, . . . }, we establish explicit lower bounds on n to guarantee the existence of maximum packings with any possible leave whose cycle lengths belong to S. | en_US |
| dc.description.reviewstatus | Reviewed | en_US |
| dc.description.scholarlevel | Faculty | en_US |
| dc.description.sponsorship | Research of Yanxun Chang is supported by NSFC grant 11431003; research of Peter Dukes is supported by NSERC grant 312595–2017; research of Tao Feng is supported by NSFC grant 11471032; research of this paper was also partially supported by 111 Project of China, grant number B16002. | en_US |
| dc.identifier.citation | Chang, Y., Dukes, P. J., & Feng, T. (2019). Leaves for packings with block size four. arXiv. https://arxiv.org/abs/1905.12151 | en_US |
| dc.identifier.uri | https://arxiv.org/abs/1905.12151 | |
| dc.identifier.uri | http://hdl.handle.net/1828/12746 | |
| dc.language.iso | en | en_US |
| dc.publisher | arXiv | en_US |
| dc.subject.department | Department of Mathematics and Statistics | |
| dc.title | Leaves for packings with block size four | en_US |
| dc.type | Preprint | en_US |