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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2507.08114 |
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Sommario:
- The biclique partition number of a graph \(G\), denoted \( \operatorname{bp}(G)\), is the minimum number of biclique subgraphs that partition the edge set of \(G\). The Graham-Pollak theorem states that the complete graph on \( n \) vertices cannot be partitioned into fewer than \( n-1 \) bicliques. In this note, we show that for any split graph \( G \), the biclique partition number satisfies \( \operatorname{bp}(G) = \operatorname{mc}(G^c) - 1 \), where \( \operatorname{mc}(G^c) \) denotes the number of maximal cliques in the complement of \( G \). This extends the celebrated Graham-Pollak theorem to a broader class of graphs.