Incidence-free sets and edge domination in incidence graphs
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866912850057887744 |
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| author | Spiro, Sam Adriaensen, Sam Mattheus, Sam |
| author_facet | Spiro, Sam Adriaensen, Sam Mattheus, Sam |
| contents | A set of edges $Γ$ of a graph $G$ is an edge dominating set if every edge of $G$ intersects at least one edge of $Γ$, and the edge domination number $γ_e(G)$ is the smallest size of an edge dominating set. Expanding on work of Laskar and Wallis, we study $γ_e(G)$ for graphs $G$ which are the incidence graph of some incidence structure $D$, with an emphasis on the case when $D$ is a symmetric design. In particular, we show in this latter case that determining $γ_e(G)$ is equivalent to determining the largest size of certain incidence-free sets of $D$. Throughout, we employ a variety of combinatorial, probabilistic and geometric techniques, supplemented with tools from spectral graph theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_14339 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Incidence-free sets and edge domination in incidence graphs Spiro, Sam Adriaensen, Sam Mattheus, Sam Combinatorics 05B05, 05C70 A set of edges $Γ$ of a graph $G$ is an edge dominating set if every edge of $G$ intersects at least one edge of $Γ$, and the edge domination number $γ_e(G)$ is the smallest size of an edge dominating set. Expanding on work of Laskar and Wallis, we study $γ_e(G)$ for graphs $G$ which are the incidence graph of some incidence structure $D$, with an emphasis on the case when $D$ is a symmetric design. In particular, we show in this latter case that determining $γ_e(G)$ is equivalent to determining the largest size of certain incidence-free sets of $D$. Throughout, we employ a variety of combinatorial, probabilistic and geometric techniques, supplemented with tools from spectral graph theory. |
| title | Incidence-free sets and edge domination in incidence graphs |
| topic | Combinatorics 05B05, 05C70 |
| url | https://arxiv.org/abs/2211.14339 |