Connected forcing density and related problems
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866916844625985536 |
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| author | Brimkov, Boris Davila, Randy Schuerger, Houston |
| author_facet | Brimkov, Boris Davila, Randy Schuerger, Houston |
| contents | A connected forcing set of a graph is a zero forcing set that induces a connected subgraph. In this paper, we introduce and study CF-dense graphs -- graphs in which every vertex belongs to some minimum connected forcing set. We identify several CF-dense graph families and investigate the relationships between CF-density and analogous notions in zero forcing and total forcing. We also characterize CF-dense trees and give a formula for the number of distinct connected forcing sets in trees. Finally, we analyze when CF-density is preserved under graph operations such as Cartesian products, joins, and coronas. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_11194 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Connected forcing density and related problems Brimkov, Boris Davila, Randy Schuerger, Houston Combinatorics 05C15, 05C30, 05C57, 05C76 A connected forcing set of a graph is a zero forcing set that induces a connected subgraph. In this paper, we introduce and study CF-dense graphs -- graphs in which every vertex belongs to some minimum connected forcing set. We identify several CF-dense graph families and investigate the relationships between CF-density and analogous notions in zero forcing and total forcing. We also characterize CF-dense trees and give a formula for the number of distinct connected forcing sets in trees. Finally, we analyze when CF-density is preserved under graph operations such as Cartesian products, joins, and coronas. |
| title | Connected forcing density and related problems |
| topic | Combinatorics 05C15, 05C30, 05C57, 05C76 |
| url | https://arxiv.org/abs/2507.11194 |